Last updated at May 12, 2021 by Teachoo

Transcript

Example 12 (Introduction) Simplify tan−1 [(a cos〖x − b sinx 〗)/(b cos〖x + a sinx 〗 )], if a/b tan x > −1 We write (a cos〖x − b sinx 〗)/(b cos〖x + a sinx 〗 ) in form of tan We know that tan (x – y) = 𝑡𝑎𝑛〖𝑥 −〖 𝑡𝑎𝑛〗〖𝑦 〗 〗/(1 + 𝑡𝑎𝑛〖𝑥 𝑡𝑎𝑛𝑦 〗 ) 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 sinx 〗)/(b cos〖x + a sinx 〗 )], if a/b tan x > −1 tan−1 [(a cos〖x − b sinx 〗)/(b cos〖x + a sinx 〗 )] = tan−1 [((a cos〖x − b sinx 〗)/(b cosx ))/((b cos〖x + a sinx 〗)/(b cosx ))] = tan−1 [((𝑎 cos𝑥)/(𝑏 cos𝑥 ) − (𝑏 sin𝑥)/(𝑏 cos𝑥 ))/((𝑏 cos𝑥)/(𝑏 cos𝑥 ) + (𝑎 sin𝑥)/(𝑏 cos𝑥 ))] = tan−1 [(𝑎/(𝑏 ) − sin𝑥/cos𝑥 )/(1 + (𝑎 sin𝑥)/(𝑏 cos𝑥 ))] = tan−1 [(a/b − tanx)/(1 + a/b tanx )] = 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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Example 3 (i) Important

Example 3 (ii)

Example 4 Deleted for CBSE Board 2022 Exams

Example 5 Important Deleted for CBSE Board 2022 Exams

Example 6 Important Deleted for CBSE Board 2022 Exams

Example 7 Deleted for CBSE Board 2022 Exams

Example 8 Deleted for CBSE Board 2022 Exams

Example 9 Important

Example 10 Important Deleted for CBSE Board 2022 Exams

Example 11 Important Deleted for CBSE Board 2022 Exams

Example 12 Important Deleted for CBSE Board 2022 Exams You are here

Example 13 Important Deleted for CBSE Board 2022 Exams

Chapter 2 Class 12 Inverse Trigonometric Functions (Term 1)

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.