Question

`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta` 

Answer 1

Start by putting on a common denominator.

Explanation:

`(sin theta xx sin theta)/((1 + cos theta)xxsin theta) + ((1 + costheta)xx(1 + cos theta))/(sin theta xx (1 + cos theta))`

= `(sin^2theta + 1 + 2 cos theta + cos^2 theta)/(sin theta xx (1 + cos theta))`

Using the pythagorean identity cos²θ+sin²θ = 1

= `(2 + 2 cos theta)/(sin theta xx (1 + cos theta))`

= `(2 (1 + cos theta))/(sin theta xx (1 + cos theta))`

= `2/sin theta`

Now recall that `1/sin theta = cosec theta`

= 2 cosec θ