Question

Find the value of ${\sin }^2{50}^o+{\sin }^2{40}^o$

Answer 1

${\sin }^2{40}^o+{\sin }^2{50}^o$

Putting $\sin x=\cos ({90}^o-x)$

$x={50}^o$

$\sin {50}^o=\cos {40}^o$

${\sin }^2{50}^o={\cos }^2{40}^o$

${\sin }^2{40}^o+{\cos }^2{40}^o$

We know that

${\sin }^{2}x+{\cos }^{2}x=1$

${\sin }^2{40}^o+{\cos }^2{40}^o=1$.