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Misc 6 - Prove cos-1 12/13 + sin-1 3/5 = sin-1 56/65 - Miscellaneous

Misc. 6 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2
Misc. 6 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 3

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Misc 6 Prove cos-1 12/13 + sin-1 3/5 = sin-1 56/65 Let a = cos-1 12/13 & b = sin-1 3/5 Finding sin a, cos a Let a = cos-1 12/13 cos a = 12/13 We know that sin a = √(1 −cos^2⁡a ) = √(1−(12/13)^2 ) "=" √(25/169) = 5/13 We convert cos-1 to sin-1 & then use sin (a + b) formula Finding sin b, cos b Let b = sin-1 3/5 sin b = 3/5 We know that cos b = √(1 −sin^2⁡b ) =√(1−(3/5)^2 ) "=" √(16/25) "=" 4/5 We know that sin (a + b) = sin a cos b + cos a sin b sin (a + b) = 5/13 × 4/5 + 12/13 × 3/5 = 20/65 + 36/65 = 𝟓𝟔/𝟔𝟓 Putting sin a = 5/13 , cos a = 12/13 & sin b = 3/5 , cos b = 4/5 Thus, sin (a + b) = 56/65 a + b = sin-1 56/65 Putting values cos-1 𝟏𝟐/𝟏𝟑 + sin-1 𝟑/𝟓 = sin-1 𝟓𝟔/𝟔𝟓 Hence L.H.S = R.H.S Hence Proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.