Question

(cosec C theta-cot theta)²=1-cos theta/1+cos theta

Answer 1

1−cosΘ1+cosΘ = 1−cosΘ/1+cosΘ⋅1−cosΘ/1−cosΘ

=(1−cosΘ)^2 /1^2−cos^2Θ

We have sin^2Θ+cos2Θ=1
so sin^2Θ=1−cos^2Θ

=(1−cosΘ)^2/ sin^2Θ

=(1−cosΘ/sinΘ)^2

Separating the fractions

=(1/sinΘ−cosΘ/sinΘ)^2

=(cosecΘ−cotΘ)^2