Question 123

If $$x=\frac{\cos\theta}{1-\sin\theta}$$, then $$\frac{\cos\theta}{1+\sin\theta}$$ is equal to

Solution

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

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

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

=> $$x=\frac{1 + \sin\theta}{\cos\theta}$$

$$\therefore$$ $$\frac{\cos\theta}{1 + \sin\theta} = \frac{1}{x}$$

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