Discussion

If \(\cot \theta = 7/8\), the value of \(\frac{(1+\sin\theta)(1-\sin\theta)}{(1+\cos\theta)(1-\cos\theta)}\) is:

Answer: B

The expression simplifies using the difference of squares formula, \((a+b)(a-b) = a^2 - b^2\).

Numerator = \(1 - \sin^2\theta = \cos^2\theta\).

Denominator = \(1 - \cos^2\theta = \sin^2\theta\).

The expression becomes \(\frac{\cos^2\theta}{\sin^2\theta} = \cot^2\theta\).

Given \(\cot \theta = 7/8\), the value is \((\frac{7}{8})^2 = \frac{49}{64}\).

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