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

Given: $ (cos^{2}67^{o} – sin^{2}23^{o})$.

To do: To find its value. 

As known $cos(90^{o}-\theta)=sin\theta$

$\Rightarrow cos(90^{o}-23^{o})=sin23^{o}$

$\Rightarrow cos67^{o}=sin23^{o}$

$\Rightarrow cos^{2}67^{o}=sin^{2}23^{o}$

$\therefore (cos^{2}67^{o} – sin^{2}23^{o}) =sin^{2}23^{o}-sin^{2}23^{o}=0$