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If tan^2theta=2tan^2varphi+1,t h e ncos2...

If `tan^2theta=2tan^2varphi+1,t h e ncos2theta+sin^2varphi` equals `-1` (b) 0 (c) 1 (d) none of these

A

`-1`

B

0

C

1

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
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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