Last updated at May 29, 2018 by Teachoo

Transcript

Example 5 Express tan-1 cosx/(1 − sinx ) , - π/2 < x < 3π/2 in the simplest form Lets first calculate cos x & 1 – sin x Solving tan-1 (cosx/(1 〖− sin〗x )) = tan-1 [(cos2 x/2 − sin2 x/2)/(1 − (2 〖sin 〗〖x/2 cos〖 x/2〗 〗 ) )] = tan-1 [(cos2 x/2 − sin2 x/2)/(1 − 2 〖sin 〗〖x/2 〖 cos 〗〖x/2〗 〗 )] = tan-1 [(cos2 x/2 − sin2 x/2)/(cos2 x/2 + sin2 x/2 − 2 〖sin 〗〖x/2 cos〖 x/2〗 〗 )] = tan-1 [(cos x/2 + sin x/2)(cos x/2 − sin x/2)/(cos x/2 − sin x/2)^2 ] = tan-1 [((cos x/2 + sin x/2))/((cos x/2 − sin x/2) )] Dividing by cos 𝑥/2 = tan-1 ((cos〖 𝑥/( 2 )〗/〖𝑐𝑜𝑠 〗〖 𝑥/2〗 + sin〖 𝑥/( 2 )〗/〖𝑐𝑜𝑠 〗〖 𝑥/2〗 )/(𝑐𝑜𝑠〖 𝑥/( 2 )〗/〖𝑐𝑜𝑠 〗〖 𝑥/2〗 − 𝑠𝑖𝑛〖 𝑥/( 2 )〗/〖𝑐𝑜𝑠 〗〖 𝑥/2〗 )) = tan-1 [(1 + 〖tan 〗〖𝑥/2〗)/(1 − tan〖 𝑥/2〗 )] = tan-1 [(1 + 〖tan 〗〖𝑥/2〗)/(1 − 〖1. tan〗〖 𝑥/2〗 )] = tan-1 ((𝑡𝑎𝑛〖 𝜋/4〗 + 〖𝑡𝑎𝑛 〗〖𝑥/2〗)/( 1− 〖𝑡𝑎𝑛 〗〖𝜋/4 〗.〖 𝑡𝑎𝑛 〗〖𝑥/2〗 )) = tan -1 [tan(π/4+x/2 ) ] = π/4+x/2

Chapter 2 Class 12 Inverse Trigonometric Functions

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.