Question

prove that cos theta minus sin theta + 1 by cos theta + sin theta minus 1 equal to cosec theta + cot theta

Answer 1

Answer:

proof given below:

Explanation:

Taking conjugate of the denominator

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

=(1−cosΘ)212−cos2Θ

We have sin2Θ+cos2Θ=1
so sin2Θ=1−cos2Θ

=(1−cosΘ)2sin2Θ

=(1−cosΘsinΘ)2

Seperating the fractions

=(1sinΘ−cosΘsinΘ)2

=(cscΘ−cotΘ)2

Answer 2

your answer for above question