Question

how to solve this???​

Answer 1

Step-by-step explanation:

$\large\sf{\sqrt{\frac{1+sin\theta}{1-sin\theta}}+\sqrt{\frac{1-sin\theta}{1+sin\theta}}}$

$\large \sf{=\frac{\left(\sqrt{1+sin\theta}\right)^{2}+\left(\sqrt{1-sin\theta}\right)^{2}}{\sqrt{(1-sin\theta)(1+sin\theta)}}}$

$\large\sf{=\frac{1-sin\theta+1+sin\theta}{\sqrt{1^{2}-sin^{2}\theta}}}$

$\large \sf{=\frac{2}{\sqrt{cos^{2}\theta}}}$

$\large\sf{= \frac{2}{cos\theta}}$

$\large\sf{= 2sec\theta}$

$\large\sf{=RHS}$

Therefore,

$\large\sf\red{\sqrt{\frac{1+sin\theta}{1-sin\theta}}+\sqrt{\frac{1-sin\theta}{1+sin\theta}}=2sec\theta}$