Question

The value of ${\sin }^2{25}^{\circ }+{\sin }^2{65}^{\circ }$ is equal to

• A. $0$
• B. $2{\sin }^2{25}^{\circ }$
• C. $2{\cos }^2{65}^{\circ }$
• D. $1$

Answer 1

The correct option is D $1$

It is known that, $sin({90}^o-x)=cos{x}^o$

According to the given condition,

${\sin }^2{25}^{\circ }+{\sin }^2{65}^{\circ }={\sin }^2({90}^{\circ }-{65}^{\circ })+{\sin }^2{65}^{\circ }={\cos }^2{65}^{\circ }+{\sin }^2{65}^{\circ }=1$