Check sibling questions

Example 10 - Show that sin-1 3/5 - sin-1 8/17  = cos-1 84/85

Example 10 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2
Example 10 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 3

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Transcript

Example 10 Show that sin−1 3/5 − sin-1 8/17 = cos−1 84/85 Let sin−1 3/5 = a and sin−1 8/17 = b So, we need to prove a − b = cos−1 84/85 cos (a − b) = 84/85 cos a cos b + sin a sin b = 84/85 Finding cos a and cos b Let sin−1 𝟑/𝟓 = a sin a = 3/5 cos a = √(1−sin2 a) = √(1 −(3/5)^2 ) = √(1 − 9/25) = 4/5 Let sin−1 𝟖/𝟏𝟕 = b sin b = 8/17 cos b = √(1 −sin2 b) = √(1 −(8/17)^2 ) = √(1 −64/289) = 15/17 Let sin−1 𝟖/𝟏𝟕 = b sin b = 8/17 cos b = √(1 −sin2 b) = √(1 −(8/17)^2 ) = √(1 −64/289) = 15/17 Now, cos a cos b + sin a sin b = 4/5 × 15/17 + 3/5 × 8/17 = (60 + 24)/(17 × 5) = 𝟖𝟒/𝟖𝟓 = RHS Hence proved Putting cos a = 4/5 & sin a = 3/5 and cos b = 15/13 & sin b = 8/17

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.