{"id":641,"date":"2023-10-22T11:37:32","date_gmt":"2023-10-22T06:07:32","guid":{"rendered":"https:\/\/samacheer-kalvi.com\/?p=641"},"modified":"2023-11-10T10:41:24","modified_gmt":"2023-11-10T05:11:24","slug":"samacheer-kalvi-9th-maths-guide-chapter-6-ex-6-2","status":"publish","type":"post","link":"https:\/\/samacheer-kalvi.com\/samacheer-kalvi-9th-maths-guide-chapter-6-ex-6-2\/","title":{"rendered":"Samacheer Kalvi 9th Maths Guide Chapter 6 Trigonometry Ex 6.2"},"content":{"rendered":"

Students can download Maths Chapter 6 Trigonometry Ex 6.2 Questions and Answers, Notes, Samacheer Kalvi 9th Maths Guide<\/a> Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.<\/p>\n

Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 6 Trigonometry Ex 6.2<\/h2>\n

Question 1.
\nVerify the following equalities:
\n(i) sin\u00b2 60\u00b0 + cos\u00b2 60\u00b0 = 1
\nSolution:
\nsin 60\u00b0 = \\(\\frac{\u221a3}{2}\\); cos 60\u00b0 = \\(\\frac{1}{2}\\)
\nL.H.S = sin\u00b2 60\u00b0 + cos\u00b2 60\u00b0
\n\"Samacheer
\nL.H.S = R.H.S
\nHence it is proved.<\/p>\n

\"Samacheer<\/p>\n

(ii) 1 + tan\u00b2 30\u00b0 = sec\u00b2 30\u00b0
\nSolution:
\ntan 30\u00b0 = \\(\\frac{1}{\u221a3}\\); sec 30\u00b0 = \\(\\frac{2}{\u221a3}\\)
\nL.H.S = 1 + tan\u00b2 30\u00b0
\n\"Samacheer
\n\u2234 L.H.S = R.H.S
\nHence it is proved.<\/p>\n

(iii) cos 90\u00b0 = 1 – 2sin\u00b2 45\u00b0 = 2cos\u00b2 45\u00b0 – 1
\nSolution:
\ncos 90\u00b0 = 0, sin 45\u00b0 = \\(\\frac{1}{\u221a2}\\), cos 45\u00b0 = \\(\\frac{1}{\u221a2}\\)
\ncos 90\u00b0 = 0 ……. (1)
\n1 – 2 sin\u00b2 45\u00b0 = 1 – 2 (\\(\\frac{1}{\u221a2}\\))\u00b2
\n= 1 – 2 \u00d7 \\(\\frac{1}{2}\\)
\n= 1 – 1 = 0 \u2192 (2)
\n2 cos\u00b2 45\u00b0 – 1 = 2(\\(\\frac{1}{\u221a2}\\))\u00b2 – 1
\n= \\(\\frac{2}{2}\\) – 1
\n= \\(\\frac{2 – 2}{2}\\) = 0 \u2192 (3)
\nFrom (1), (2) and (3) we get
\ncos 90\u00b0 = 1 – 2 sin\u00b2 45\u00b0 = 2 cos\u00b2 45\u00b0 – 1
\nHence it is proved.<\/p>\n

\"Samacheer<\/p>\n

(iv) sin 30\u00b0 cos 60\u00b0 + cos 30\u00b0 sin 60\u00b0 = sin 90\u00b0
\nSolution:
\nsin 30\u00b0 = \\(\\frac{1}{2}\\); cos 60\u00b0 = \\(\\frac{1}{2}\\); cos 30\u00b0 = \\(\\frac{\u221a3}{2}\\); sin 60\u00b0 = \\(\\frac{\u221a3}{2}\\); sin 90\u00b0 = 1
\nL.H.S = sin 30\u00b0 cos 60\u00b0 + cos 30\u00b0 sin 60\u00b0
\n\"Samacheer
\n= 1
\nR.H.S = sin 90\u00b0 = 1
\nL.H.S = R.H.S
\nHence it is proved.<\/p>\n

\"Samacheer<\/p>\n

Question 2.
\nFind the value of the following:
\n(i) \\(\\frac{tan 45\u00b0}{cosec 30\u00b0}\\) + \\(\\frac{sec 60\u00b0}{cot 45\u00b0}\\) – \\(\\frac{5 sin 90\u00b0}{2 cos 0\u00b0}\\)
\n(ii) (sin 90\u00b0 + cos 60\u00b0 + cos 45\u00b0) \u00d7 (sin 30\u00b0 + cos 0\u00b0 – cos 45\u00b0)
\n(iii) sin\u00b230\u00b0 – 2 cos\u00b3 60\u00b0 + 3 tan4<\/sup> 45\u00b0
\nSolution:
\n(i) tan 45\u00b0 = 1, cosec 30\u00b0 = 2; sec 60\u00b0 = 2; cot 45\u00b0 = 1; tan 45\u00b0, sin 90\u00b0 = 1; cos 0\u00b0 = 1
\n\"Samacheer
\n= 0<\/p>\n

(ii) sin 90\u00b0 = 1; cos 60\u00b0 = \\(\\frac{1}{2}\\); cos 45\u00b0 = \\(\\frac{1}{\u221a2}\\); sin 30\u00b0 = \\(\\frac{1}{2}\\); cos 0\u00b0 = 1
\n(sin 90\u00b0 + cos 60\u00b0 + cos 45\u00b0) \u00d7 (sin 30\u00b0 + cos 0\u00b0 – cos 45\u00b0)
\n\"Samacheer
\n= \\(\\frac{7}{4}\\)<\/p>\n

\"Samacheer<\/p>\n

(iii) sin 30\u00b0 = \\(\\frac{1}{2}\\); cos 60\u00b0 = \\(\\frac{1}{2}\\); tan 45\u00b0 = 1
\nsin\u00b2 30\u00b0 – 2 cos\u00b3 60\u00b0 + 3 tan4<\/sup> 45\u00b0
\n\"Samacheer
\n= 3<\/p>\n

\"Samacheer<\/p>\n

Question 3.
\nVerify cos 3 A = 4 cos\u00b3 A – 3 cos A, when A = 30\u00b0
\nSolution:
\nL.H.S = cos 3 A
\n= cos 3 (30\u00b0)
\n= cos 90\u00b0
\n= 0
\nR.H.S = 4 cos\u00b3 A – 3 cos A
\n= 4 cos\u00b3 30\u00b0 – 3 cos 30\u00b0
\n\"Samacheer
\n= 0
\n\u2234 L.H.S = R.H.S
\nHence it is proved.<\/p>\n

\"Samacheer<\/p>\n

Question 4.
\nFind the value of 8 sin2x, cos 4x, sin 6x, when x = 15\u00b0.
\nSolution:
\n8 sin 2x cos 4x sin 6x = 8 sin 2 (15\u00b0) \u00d7 cos 4 (15\u00b0) \u00d7 sin (6 \u00d7 15\u00b0)
\n= 8 sin 30\u00b0 \u00d7 cos 60\u00b0 \u00d7 sin 90\u00b0
\n= 8 \u00d7 \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{2}\\) \u00d7 1
\n= 2<\/p>\n

\"Samacheer<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can download Maths Chapter 6 Trigonometry Ex 6.2 Questions and Answers, Notes, Samacheer Kalvi 9th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams. Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 6 Trigonometry Ex 6.2 Question …<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[3],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/posts\/641"}],"collection":[{"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/comments?post=641"}],"version-history":[{"count":1,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/posts\/641\/revisions"}],"predecessor-version":[{"id":49449,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/posts\/641\/revisions\/49449"}],"wp:attachment":[{"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/media?parent=641"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/categories?post=641"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheer-kalvi.com\/wp-json\/wp\/v2\/tags?post=641"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}