Question

The value of $\frac{\left({\cot }^{2}5\right)\left({\cos }^{2}5\right)}{({\cot }^{2}5-{\cos }^{2}5)}$.is equal to

Answer 1

${\cot }^2\theta -{\cos }^2\theta$

$=\frac{{\cos }^2\theta }{{\sin }^2\theta }-{\cos }^2\theta$

$={\cos }^2\theta \left(\frac{1-{\sin }^2\theta }{{\sin }^2\theta }\right)$

$=\frac{{\cos }^2\theta \cdot {\cos }^2\theta }{{\sin }^2\theta }$

$={\cot }^2\theta {\cos }^2\theta$

$\therefore \frac{{\cot }^2\theta {\cos }^2\theta }{{\cot }^2\theta -{\cos }^2\theta }=1$

By putting $\theta =5^{\circ }$

$\frac{\left({\cot }^{2}5\right)\left({\cos }^{2}5\right)}{({\cot }^{2}5-{\cos }^{2}5)}=1$.