If `(3-tan^2(pi/7))/(1-tan^2(pi/7))=kcos(pi/7)` then the value of `k` is (a)1 (b) 2 (c) 3 (d) 4

Explanation

`theta=pi/7`

`3theta=3/7pi=pi-4/7pi=pi-4theta`

`sin3theta=sin(pi-4theta)=sin4theta`

`sin3theta=sin4theta`

`3sintheta-4sin^3theta=2sin2thetacos2theta`

`3sintheta-4sin3theta=4sinnthetacosthetacos2theta`

`3-4ssin^2theta=4costheta(2cos^2theta-1)`

`thetacos^3theta-4costheta=3-4(1-cos^2theta)`

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