Question

If cot θ = 7/8, evaluate \(\frac{(1+sinθ)(1-sin\theta)}{(1+cos\theta)(1-cos\theta)}\).

Answer 1

Now,

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

\(=\frac{cos^2\theta}{sin^2\theta}=(\frac{cos\theta}{sin\theta})^2\)

= cot²θ

= \((\frac{7}{8})^2\) = \(\frac{49}{64}\)