If $\frac{(1-\cos \theta)}{\sin \theta}=\frac{1}{5}$, then what will be the value of $\frac{(1+\cos \theta)}{\sin \theta} ?$
Answer & explanation
Correct answer: option 1
$\frac{(1-\cos \theta)}{\sin \theta}=\frac{1}{5}$
As , \(\frac{1 - cosθ }{sinθ }\)
= cosecθ - cotθ
cosecθ - cotθ = \(\frac{1 }{5}\)
Using , cosec2θ - cot2θ = 1
So , (cosecθ - cotθ ) . (cosecθ + cotθ ) = 1
\(\frac{1 }{5}\) . (cosecθ + cotθ ) = 1
(cosecθ + cotθ ) = 5
Hence ,
\(\frac{1 + cosθ }{sinθ }\) = 5