Question

Evaluate:

${\cos }^2{25}^{\circ }–{\sin }^2{65}^{\circ }–{\tan }^2{45}^{\circ }$

Answer 1

According to the question we have

${\cos }^2{25}^{\circ }–{\sin }^2{65}^{\circ }–{\tan }^2{45}^{\circ }$

$=\left[\cos \right({90}^{\circ }–{65}^{\circ }){]}^2–{\sin }^2{65}^{\circ }–({\tan }^2{45}^{\circ }{)}^2$

$={\sin }^2{65}^{\circ }–{\sin }^2{65}^{\circ }–1^2$

$=0–1$

$=-1$