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If t a n^2theta=2tan^2phi+1 , prove tha...

If `t a n^2theta=2tan^2phi+1` , prove that `cos2theta+sin^2phi=0.`

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Given:-
`tan^2theta = 2 tan^2phi + 1….(i)`
we know that,
`=>cos 2theta = (1 – tan^2theta)/(1 + tan^2theta)`
`= [1 – (2 tan^2phi + 1)]/ [1 + (2 tan^2phi + 1)]`[from(i)]
`= (-2 tan^2phi)/ (2 + 2 tan^2phi)`
`= (-2 tan^2phi)/ (2(1 + tan^2phi)`
`= -tan^2phi/ (sec^2phi)`
...
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