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Question 125
The expression $$\sqrt{\frac{1+sin\ \theta}{1-sin\ \theta}}+\sqrt{\frac{1-sin\ \theta}{1+sin\ \theta}}$$ is equal to
Solution
Expression : $$\sqrt{\frac{1+sin\ \theta}{1-sin\ \theta}}+\sqrt{\frac{1-sin\ \theta}{1+sin\ \theta}}$$
= $$\frac{(\sqrt{1+sin\theta})^2+(\sqrt{1-sin\theta})^2}{(\sqrt{1-sin\theta})(\sqrt{1+sin\theta})}$$
= $$\frac{(1+sin\theta)+(1-sin\theta)}{\sqrt{1-sin^2\theta}}$$
= $$\frac{2}{cos\theta}=2sec\theta$$
=> Ans - (A)
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