Question

The value of \[\sqrt{\frac{1 + \cos \theta}{1 - \cos \theta}}\]

Options

•  cot θ − cosec θ

•  cosec θ + cot θ

• cosec² θ + cot² θ

•  (cot θ + cosec θ)²

Answer 1

The given expression is `sqrt ((1+cosθ)/(1-cos θ))` 

Multiplying both the numerator and denominator under the root by` (1+cosθ )`, we have

`sqrt (((1+cosθ)(1+cosθ))/((1+cosθ)(1-cos θ)))` 

`=sqrt ((1+cosθ)^2/ ((1-cos^2 θ))` 

`=sqrt((1+cos θ)^2/sin^2θ` 

`=(1+cos θ)/(sinθ)` 
= `1/sinθ+cosθ/sinθ`

= `cosecθ+cotθ`