STD 11 - 3. trignometrical ratios,functions and identities — JEE कक्षा 11 साइन्स — Question

$\Rightarrow 1 + {\tan ^2}\theta  = 2\,(1 + {\tan ^2}\phi )$

$\Rightarrow$ ${\sec ^2}\theta  = 2{\sec ^2}\phi $

$\Rightarrow {\cos ^2}\phi = 2{\cos ^2}\theta $

$\Rightarrow$ ${\cos ^2}\phi = 1 + \cos 2\theta  $

$\Rightarrow {\sin ^2}\phi   + \cos 2\theta  = 0$.

ट्रिक : माना $\theta  = {45^o}$ तब $\phi = 0$

$\therefore \;\cos (2 \times {45^o}) + {\sin ^2}0 = 0 + 0 = 0$.