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If (3-tan^2pi/7)/(1-tan^2pi/7)=kcospi/7 ...

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

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
D
Let `theta=(pi)/(7)`
`rArr 3theta=pi-4theta`
`rArr sin3 theta=sin4theta`
`rArr 3sin theta-4 sin^(3)theta=4sinthetacos theta cos 2theta`
`rARr 3-4sin^(2)theta=4cos theta(2cos^(2)theta-1)`
`rArr 8cos^(3)theta-4cos theta=4cos^(2)theta-1`
`rArr 4costheta=(4cos^(2)theta-1)/(2cos^(2)theta-1)=(3-tan^(2)theta)/(1-tan^(2)theta)`
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