Question

The value of the expression $\left(\text{cosec} 50^{\circ}+\sqrt{3} \sec 50^{\circ}\right)$ is equal to

Answer 1

$y=2\left[\frac{1}{2 \sin 50^{\circ}}+\frac{\sqrt{3}}{2 \cos 50^{\circ}}\right]$
$=2\left[\frac{\cos 60^{\circ}}{\sin 50^{\circ}}+\frac{\sin 60^{\circ}}{\cos 50^{\circ}}\right]=4 \times \frac{\cos 10^{\circ}}{\sin 100^{\circ}}=4$