Question

Q.4 Prove the following identity
.
Tan A + Sec A
----------------- = Tan A × sec A
Cos A + cot A​

Answer 1

Answer:

$\frac{tan A + sec A}{cos A + cot A}$

$= \frac{(\frac{sin A}{cos A} + \frac{1}{cos A})}{(cos A + \frac{cos A}{sin A})}$

$= \frac{\frac{sin A + 1}{cos A}}{\frac{cos A . sin A + cos A}{sin A}}$

$= \frac{sin A + 1}{cos A} * \frac{sin A}{cos A(sin A + 1)}$

$= \frac{1}{cos A} * \frac{sin A}{cos A}$

$= sec A . tan A$

$= tan A . sec A$

Hope this helps!! Pls mark as brainliest!