Question

Evaluate :
${\left[\frac{\sin 35°}{\cos 55°}\right]}^2+{\left[\frac{\cos 55°}{\sin 35°}\right]}^2-2\cos 60°$

Answer 1

Evaluating the given expression:

${\left[\frac{\sin 35°}{\cos 55°}\right]}^2+{\left[\frac{\cos 55°}{\sin 35°}\right]}^2-2\cos 60°$

${\left[\frac{\sin 35°}{\sin (90°-55°)}\right]}^2+{\left[\frac{\cos 55°}{\cos (90°-35°)}\right]}^2-2\cos 60°\left[\because \cos A=\sin (90°-A),\sin A=\cos (90°-A)\right]$

$={\left[\frac{\sin 35°}{\sin 35°}\right]}^2+{\left[\frac{\cos 55°}{\cos 55°}\right]}^2-2\cos 60°$

We know that, $\cos 60°=\frac{1}{2}$

$=1^2+1^2-2\times \frac{1}{2}$

$=1+1-1$

$=2-1$

$=1$

Hence, the value of the given expression is $1$.