Question

Proove that 1/1-sin theta + 1/1+cos theta = 2×sec square theta ​

Answer 1

Step-by-step explanation:

We need to prove that,

$\dfrac{1}{1-\sin\theta}+\dfrac{1}{1+\sin\theta}=2\times \sec^2\theta$

Taking LHS,

$\dfrac{1}{1-\sin\theta}+\dfrac{1}{1+\sin\theta}\\\\=\dfrac{(1+\sin\theta)+(1-\sin\theta)}{(1-\sin\theta)(1+\sin\theta)}\\\\=\dfrac{2}{1-\sin^2\theta}\\\\\text{As}\ 1-\sin^2\theta=\cos^2\theta\\\\=\dfrac{2}{\cos^2\theta}\\\\\text{As}\ \dfrac{1}{\cos^2\theta}=\sec^2\theta\\\\=2\sec^2\theta\\\\=RHS$

Hence, LHS = RHS.