Question

Prove the identity $\frac{\sin \theta }{cosec\theta }+\frac{\cos \theta }{\sec \theta }=1$

Answer 1

L.H.S $=\frac{\sin \theta }{cosec\theta }+\frac{\cos \theta }{\sec \theta }$

$=\frac{\sin \theta }{\frac{1}{\sin \theta }}+\frac{\cos \theta }{\frac{1}{\cos \theta }}$

$={\sin }^2\theta +{\cos }^2\theta$

$=1$ = R.H.S

Hence Proved.