If $\frac{(1-\cos \theta)}{\sin \theta}=\frac{1}{5}$, then what will be the value of $\frac{(1+\cos \theta)}{\sin \theta} ?$

5

$\frac{(1-\cos \theta)}{\sin \theta}=\frac{1}{5}$

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