Question 63

The value of $$\frac{sin\theta}{1+cos\theta}+\frac{sin\theta}{1-cos\theta}$$ is

Solution

Expression : $$\frac{sin\theta}{1+cos\theta}+\frac{sin\theta}{1-cos\theta}$$

= $$\frac{sin\theta(1-cos\theta)+sin\theta(1+cos\theta)}{(1+cos\theta)(1-cos\theta)}$$

= $$\frac{(sin\theta-sin\theta cos\theta)+(sin\theta+sin\theta cos\theta)}{1-cos^2\theta}$$

= $$\frac{2sin\theta}{sin^2\theta}$$

= $$\frac{2}{sin\theta}=2cosec\theta$$

=> Ans - (D)

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