Question

Prove the following trigonometric identities.

$\left(1+\cot A+\tan A\right)\left(\sin A-\cos A\right)=\frac{\sec A}{{\mathrm{cosec}}^{2}A}-\frac{\mathrm{cosec}A}{{\sec }^{2}A}=\sin A\tan A-\cot A\cos A$

Answer 1

We have prove that

We know that,

So,

Now,

Hence proved.