Examples

Chapter 2 Class 12 Inverse Trigonometric Functions
Serial order wise

### Transcript

Question 6 (Introduction) Simplify tan−1 [(a cos⁡〖x − b sin⁡x 〗)/(b cos⁡〖x + a sin⁡x 〗 )], if a/b tan x > −1 We write (a cos⁡〖x − b sin⁡x 〗)/(b cos⁡〖x + a sin⁡x 〗 ) in form of tan We know that tan (x – y) = 𝑡𝑎𝑛⁡〖𝑥 −〖 𝑡𝑎𝑛〗⁡〖𝑦 〗 〗/(1 + 𝑡𝑎𝑛⁡〖𝑥 𝑡𝑎𝑛⁡𝑦 〗 ) We need denominator in form 1 + tan x tan y Hence, we need 1 instead of b cos x So dividing both numerator and denominator by b cos x Question 6 Simplify tan−1 [(a cos⁡〖x − b sin⁡x 〗)/(b cos⁡〖x + a sin⁡x 〗 )], if a/b tan x > −1 tan−1 [(a cos⁡〖x − b sin⁡x 〗)/(b cos⁡〖x + a sin⁡x 〗 )] = tan−1 [((a cos⁡〖x − b sin⁡x 〗)/(b cos⁡x ))/((b cos⁡〖x + a sin⁡x 〗)/(b cos⁡x ))] = tan−1 [((𝑎 cos⁡𝑥)/(𝑏 cos⁡𝑥 ) − (𝑏 sin⁡𝑥)/(𝑏 cos⁡𝑥 ))/((𝑏 cos⁡𝑥)/(𝑏 cos⁡𝑥 ) + (𝑎 sin⁡𝑥)/(𝑏 cos⁡𝑥 ))] = tan−1 [(𝑎/(𝑏 ) − sin⁡𝑥/cos⁡𝑥 )/(1 + (𝑎 sin⁡𝑥)/(𝑏 cos⁡𝑥 ))] = tan−1 [(a/b − tan⁡x)/(1 + a/b tan⁡x )] = tan−1 a/b – tan−1 (tan x) = tan−1 𝐚/𝐛 − x Using equation tan−1((𝒙 − 𝒚)/(𝟏 + 𝒙𝒚)) = tan−1 x – tan−1 y Replacing x with 𝑎/𝑏 and y with tan x

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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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.