Question

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

Answer 1

Answer: 4

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