यदि {tan ^2}theta = 2{tan ^2}phi | vedclass

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Question

${	an ^2}	heta  = 2{	an ^2}\phi + 1 $

$\Rightarrow 1 + {	an ^2}	heta  = 2\,(1 + {	an ^2}\phi )$

$\Rightarrow$ ${\sec ^

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${	an ^2}	heta  = 2{	an ^2}\phi + 1 $

$\Rightarrow 1 + {	an ^2}	heta  = 2\,(1 + {	an ^2}\phi )$

$\Rightarrow$ ${\sec ^2}	heta  = 2{\sec ^2}\phi $

$\Rightarrow {\cos ^2}\phi = 2{\cos ^2}	heta $

$\Rightarrow$ ${\cos ^2}\phi = 1 + \cos 2	heta  $

$\Rightarrow {\sin ^2}\phi   + \cos 2	heta  = 0$.

ट्रिक : माना $	heta  = {45^o}$ तब $\phi = 0$

$	herefore \;\cos (2 	imes {45^o}) + {\sin ^2}0 = 0 + 0 = 0$.

यदि ${\tan ^2}\theta = 2{\tan ^2}\phi + 1,$ तब $\cos 2\theta + {\sin ^2}\phi $ बराबर है

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