\(\sqrt { \frac{1- cos θ}{1+cosθ} } × \sqrt { \frac{cosecθ - cosθ}{cosec θ+cot θ} } = \frac{1-r}{1+r}\), find the value of r.
Answer & explanation
Correct answer: option 2
⇒ \(\sqrt { \frac{1- cos θ}{1+cosθ} } × \sqrt {\frac{\frac{1}{sinθ}-\frac{cosθ}{sinθ}}{\frac{1}{sinθ}+\frac{cosθ}{sinθ}}} = \frac{1-r}{1+r}\)
⇒ \(\sqrt { \frac{1- cos θ}{1+cosθ} } × \sqrt { \frac{1 - cosθ}{1+cos θ} } = \frac{1-r}{1+r}\)
⇒ \(\frac{1- cos θ}{1+cosθ} = \frac{1-r}{1+r}\)
r = cos θ