Question

$\frac{1}{1 + sin} + \frac{1}{1 - sin} = {2 \sec }^{2}$
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Answer 1

Take LHS:

1-sin+1+sin/1²-sin²

2/1-sin²

We know that cos²=1-sin²

Therefore

2/cos²

2×1/cos²

We know that sec²=1/cos²

Therefore 2sec²

Therefore LHS=RHS