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If `t a n^2theta=2t a n^2varphi+1` , prove that `cos2theta+s in^2varphi=0.`

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If `t a n^2theta=2t a n^2varphi+1` , prove that `cos2theta+s in^2varphi=0.`
A. `-1`
B. 0
C. 1
D. none of these.
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1 Answer

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Correct Answer - B
`tan^(2)theta=2tan^(2)phi+1`
or `1+tan^(2)theta=2(1+tan^(2)phi)`
`rArr sec^(2)theta=2sec^(2)phi`
`rArr cos^(2)phi=2cos^(2)phi=1=+cos2theta`
`rArr cos 2theta=cos^(2)phi-1=-sin^(2)phi`
`rArr sin^(2)phi+cos2theta=0`
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