

Examples
Example 2
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
Last updated at May 12, 2021 by Teachoo
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