Question

plz ans above question ​

Answer 1

To prove:

Let theta be A for convience.

$\frac{1}{1 - sinA } + \frac{1}{1 + sinA } = 2 { \sec }^{2} A$

Proof:

$LHS = \frac{1}{ 1 - sinA} + \frac{1}{ 1 + sinA} \\ \\ = \frac{1 + sinA + 1 - sinA}{(1 - sinA)(1 + sinA)} \\ \\ = \frac{1 + 1}{ {(1)}^{2} - { (sinA )}^{2} } \\ \\ = \frac{2}{ cos^{2} A} \\ \\ = 2 sec^{2} A \\ \\ = RHS$

Hence proved.