Question

What is the value of $co{s}^2{67}^{\circ \circ }-si{n}^2{23}^{\circ }$

Answer 1

${\cos }^2{67}^{\circ }-{\sin }^2{23}^{\circ }$

$={\cos }^2({90}^{\circ }-{23}^{\circ })-{\sin }^2{23}^{\circ }$

$={\sin }^2{23}^{\circ }-{\sin }^2{23}^{\circ }$ since $\cos (90-\theta )=\sin \theta$

$=0$