Question

What is the value of $({\cos }^2{67}^o-{\sin }^{2}23)$?

Answer 1

We know that,

$co{s}^{2}B-si{n}^{2}A=cos(A+B).cos(A-B)$

Now,

$co{s}^2{67}^{\circ }-si{n}^2{23}^{\circ }$

$=cos(67+23).cos(67-23)$

$=cos{.90}^{\circ }.cos45$

$=0.\frac{1}{\sqrt{2}}$

$=0$

$\therefore (co{s}^2{67}^{\circ }-si{n}^2{23}^{\circ })=0$