Question

Prove the following trigonometric identities.

(i) $\frac{\cos A\mathrm{cosec}A-\sin A\sec A}{\cos A+\sin A}=\mathrm{cosec}A-\sec A$

(ii) $\frac{\sin A}{\sec A+\tan A-1}+\frac{\cos A}{\mathrm{cosec}A+\cot A-1}=1$

Answer 1

(i) We have to prove

So,

Hence proved.

(ii) We have to prove

We know that,

So,

Hence proved.