Question

tan^(-1)((cos7x)/(1+sin7x))​

Answer 1

Given, x=tan−11−cos−1[−21​]+sin−121​ and y=cos[21​cos−1[81​]]

here, x=tan−11−cos−1[−21​]+sin−121​

x=4π​−32π​+6π​

⇒x=12−3π​=4−π​

y=cos[21​cos−1[81​]]

Let, cos−1[81​]=θ

⇒cosθ=81​

⇒cos2θ​=21+cosθ​

​=43​=y

⇒tanx=tan4−π​=1=3−4​×43​ as in option c.

Step-by-step explanation:

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