If $\cot heta = \frac{7}{8}$, then the value of $\frac{(1 + \sin heta)(1 - \sin heta)}{(1 + \cos heta)(1 - \cos heta)}$ is ________.

Question

If $\cot 	heta = \frac{7}{8}$, then the value of $\frac{(1 + \sin 	heta)(1 - \sin 	heta)}{(1 + \cos 	heta)(1 - \cos 	heta)}$ is ________.

Accepted Answer

Step 1: $\frac{(1 + \sin 	heta)(1 - \sin 	heta)}{(1 + \cos 	heta)(1 - \cos 	heta)} = \frac{1 - \sin^2 	heta}{1 - \cos^2 	heta} = \frac{\cos^2 	heta}{\sin^2 	heta} = \cot^2 	heta = \frac{49}{64}$

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