Check sibling questions

Example 12 - Simplify tan-1 [a cos x - b sin x / b cos x]

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


Transcript

Example 12 (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 Example 12 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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.