Question

What is the value of ${\sin }^2{25}^0+{\sin }^2{65}^0$?

Answer 1

$\sin {65}^0=\sin ({90}^0-{25}^0)=\cos {25}^0$
$\therefore {\sin }^2{25}^0+{\sin }^2{65}^0$
$={\sin }^2{25}^0+{\cos }^2{25}^0$
$=1(\because {\sin }^2\theta +{\cos }^2\theta =1)$