Discussion
If \(\cot\theta = \dfrac{7}{8}\); value of \(\dfrac{(1+\sin\theta)(1-\sin\theta)}{(1+\cos\theta)(1-\cos\theta)}\) is
Answer: C
The value is 49/64.
Multiply out the brackets and use sin2θ + cos2θ = 1:
\[ \begin{aligned} \frac{(1+\sin\theta)(1-\sin\theta)}{(1+\cos\theta)(1-\cos\theta)} &= \frac{1-\sin^{2}\theta}{1-\cos^{2}\theta} \\ &= \frac{\cos^{2}\theta}{\sin^{2}\theta} = \cot^{2}\theta \end{aligned} \]
\[ \cot^{2}\theta = (7/8)^{2} = \frac{49}{64} \]
49/58 has the right numerator but a wrong denominator, and 21/24 and 35/48 do not come from squaring 7/8.
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