{"id":28555,"date":"2021-07-06T18:08:58","date_gmt":"2021-07-06T12:38:58","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=28555"},"modified":"2022-03-02T10:30:17","modified_gmt":"2022-03-02T05:00:17","slug":"ncert-solutions-for-class-10-maths-chapter-8-ex-8-3","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.3"},"content":{"rendered":"

These NCERT Solutions for Class 10 Maths<\/a> Chapter 8 Introduction to Trigonometry Ex 8.3 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.3<\/h2>\n

\"NCERT<\/p>\n

Question 1.
\n(i) \\(\\frac{\\sin 18^{\\circ}}{\\cos 72^{\\circ}}\\)
\n(ii) \\(\\frac{\\tan 26^{\\circ}}{\\cot 64^{\\circ}}\\)
\n(iii) cos 48\u00b0 – sin 42\u00b0
\n(iv) cosec 31\u00b0 – sec 59\u00b0
\nSolution:
\n\"NCERT<\/p>\n

Question 2.
\nShow that:
\n(i) tan 48\u00b0 tan 23\u00b0 tan 42\u00b0 tan 67\u00b0 = 1
\n(ii) cos 38\u00b0 cos 52\u00b0 – sin 38\u00b0 sin 52\u00b0 = 0
\nSolution:
\n(i) LHS = tan 48\u00b0 tan 23\u00b0 tan 42\u00b0 tan 67\u00b0
\n= tan 48\u00b0 tan 23\u00b0 tan (90\u00b0 – 48\u00b0) tan (90\u00b0 – 23\u00b0)
\n= tan 48\u00b0 tan 23\u00b0 cot 48\u00b0 cot 23\u00b0 = tan 48\u00b0 tan 23\u00b0 .\\(\\frac{1}{\\tan 48^{\\circ}} \\cdot \\frac{1}{\\tan 23^{\\circ}}\\)
\n= 1 = RHS [Verified]<\/p>\n

(ii) LHS = cos 38\u00b0 cos 52\u00b0 – sin 38\u00b0 sin 52\u00b0
\n= cos 38\u00b0 cos (90\u00b0 – 38\u00b0) – sin 38\u00b0 sin (90\u00b0 – 38\u00b0)
\n= cos 38\u00b0 sin 38\u00b0- sin 38\u00b0 cos 38\u00b0 = 0 = RHS [Verified]<\/p>\n

\"NCERT<\/p>\n

Question 3.
\nIf tan 2A = cot (A – 18\u00b0), where 2A is an acute angle, find the value of A.
\nSolution:
\ntan 2A = cot (A – 18\u00b0)
\n\u21d2 cot (90\u00b0 – 2A) = cot (A – 18\u00b0) [\u2235cot (90\u00b0 – \u03b8) = tan \u03b8]
\n\u21d2 90\u00b0 – 2A = A – 18\u00b0 \u21d2 3A = 108\u00b0 \u21d2 A = \\(\\frac { 108\u00b0 }{ 3 }\\)
\n\u2234 \u2220 A = 36\u00b0<\/p>\n

Question 4.
\nIf tan A = cot B, prove that A + B = 90\u00b0.
\nSolution:
\ntan A = cot B \u21d2 tan A = tan (90\u00b0 – B) [ \u2235 tan (90\u00b0 – \u03b8) = cot \u03b8]
\n\u21d2 A = 90\u00b0 – B \u21d2 A + B = 90\u00b0 Proved<\/p>\n

Question 5.
\nIf sec 4A = cosec (A – 20\u00b0), where 4A is an acute angle, find the value of A.
\nSolution:
\nsec 4A = cosec (A – 20\u00b0)
\n\u21d2 cosec (90\u00b0 – 4A) = cosec (A – 20\u00b0) [cosec (90\u00b0 – \u03b8) = sec \u03b8]
\n\u21d2 90\u00b0 – 4A = A – 20\u00b0 \u21d2 5A = 110\u00b0
\nA = \\(\\frac { 110\u00b0 }{ 5 }\\)
\nA = 22\u00b0
\n\u2234 \u2220 A = 22\u00b0<\/p>\n

\"NCERT<\/p>\n

Question 6.
\nIf A, Band Care interior angles of a triangle ABC, then show that: sin (\\(\\frac { B+C }{ 2 }\\)) = cos \\(\\frac { A }{ 2 }\\)
\nSolution:
\nWe have given that,
\nA, B and C are the interior angles of a triangle ABC
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 7.
\nExpress sin 61\u00b0 + cos 75\u00b0 in terms of trigonometric ratios of angles between 0\u00b0 and 45\u00b0.
\nSolution:
\nsin 67\u00b0 + cos 75\u00b0
\nor sin (90\u00b0 – 23\u00b0) + cos (90\u00b0 – 15\u00b0)
\nor cos 23\u00b0 + sin 15\u00b0 (\u2235 sin (90\u00b0 – \u03b8) = cos \u03b8
\nand cos (90\u00b0 – \u03b8) = sin \u03b8)
\nNow, sin 67\u00b0 + cos 75\u00b0 in term if trigonometric ratios of angles between 0\u00b0 and 45\u00b0.
\n(cos 90\u00b0 – 67\u00b0) + (sin 90\u00b0 – 75\u00b0)
\n= cos 23\u00b0 + sin 15\u00b0<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.3 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.3 Question 1. (i) (ii) (iii) cos 48\u00b0 – sin 42\u00b0 (iv) cosec 31\u00b0 – sec 59\u00b0 Solution: …<\/p>\n

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.3<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[2],"tags":[],"yoast_head":"\nNCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.3 - MCQ Questions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.3 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.3 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.3 Question 1. (i) (ii) (iii) cos 48\u00b0 – sin 42\u00b0 (iv) cosec 31\u00b0 – sec 59\u00b0 Solution: … NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.3 Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ Questions\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/\" \/>\n<meta property=\"article:published_time\" content=\"2021-07-06T12:38:58+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-03-02T05:00:17+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@ncertsolguru\" \/>\n<meta name=\"twitter:site\" content=\"@ncertsolguru\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prasanna\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mcq-questions.com\/#website\",\"url\":\"https:\/\/mcq-questions.com\/\",\"name\":\"MCQ Questions\",\"description\":\"MCQ Questions for Class 1 to 12\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mcq-questions.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1\",\"contentUrl\":\"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1\",\"width\":170,\"height\":17,\"caption\":\"NCERT Solutions\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/#webpage\",\"url\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/\",\"name\":\"NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.3 - MCQ Questions\",\"isPartOf\":{\"@id\":\"https:\/\/mcq-questions.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/#primaryimage\"},\"datePublished\":\"2021-07-06T12:38:58+00:00\",\"dateModified\":\"2022-03-02T05:00:17+00:00\",\"author\":{\"@id\":\"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3\"},\"breadcrumb\":{\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mcq-questions.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.3\"}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3\",\"name\":\"Prasanna\",\"image\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/mcq-questions.com\/#personlogo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"caption\":\"Prasanna\"},\"url\":\"https:\/\/mcq-questions.com\/author\/prasanna\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.3 - MCQ Questions","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/","og_locale":"en_US","og_type":"article","og_title":"NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.3 - MCQ Questions","og_description":"These NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.3 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.3 Question 1. (i) (ii) (iii) cos 48\u00b0 – sin 42\u00b0 (iv) cosec 31\u00b0 – sec 59\u00b0 Solution: … NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.3 Read More »","og_url":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/","og_site_name":"MCQ Questions","article_publisher":"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/","article_published_time":"2021-07-06T12:38:58+00:00","article_modified_time":"2022-03-02T05:00:17+00:00","og_image":[{"url":"https:\/\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png"}],"twitter_card":"summary_large_image","twitter_creator":"@ncertsolguru","twitter_site":"@ncertsolguru","twitter_misc":{"Written by":"Prasanna","Est. reading time":"4 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebSite","@id":"https:\/\/mcq-questions.com\/#website","url":"https:\/\/mcq-questions.com\/","name":"MCQ Questions","description":"MCQ Questions for Class 1 to 12","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mcq-questions.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/#primaryimage","inLanguage":"en-US","url":"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1","contentUrl":"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1","width":170,"height":17,"caption":"NCERT Solutions"},{"@type":"WebPage","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/#webpage","url":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/","name":"NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.3 - MCQ Questions","isPartOf":{"@id":"https:\/\/mcq-questions.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/#primaryimage"},"datePublished":"2021-07-06T12:38:58+00:00","dateModified":"2022-03-02T05:00:17+00:00","author":{"@id":"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3"},"breadcrumb":{"@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-10-maths-chapter-8-ex-8-3\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mcq-questions.com\/"},{"@type":"ListItem","position":2,"name":"NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.3"}]},{"@type":"Person","@id":"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3","name":"Prasanna","image":{"@type":"ImageObject","@id":"https:\/\/mcq-questions.com\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","caption":"Prasanna"},"url":"https:\/\/mcq-questions.com\/author\/prasanna\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/28555"}],"collection":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/comments?post=28555"}],"version-history":[{"count":1,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/28555\/revisions"}],"predecessor-version":[{"id":33829,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/28555\/revisions\/33829"}],"wp:attachment":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/media?parent=28555"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/categories?post=28555"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/tags?post=28555"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}