Question

prove that (cosec a+sin a) (cosec a - sin a) =cot square a+cos square a

Answer 1

hey there

I am meritkshitij here.

kindly refer to given attachment

Answer 2

Solution:

To prove : (cosec A +sin A)(cosec A -sin A) = cot² A +cos² A

Proof:

LHS =(cosec A + sin A)(cosec A - sin A)
As, we know the identity : a²-b²=(a+b)(a-b)
= cosec² A - sin²A
=(1+cot² A)-(1-cos² A)         as, sin²A+cos²A=1 , cosec²A-cot²A=1
=1+cot² A-1 +cos² A
=cot² A +cos² A = RHS hence, proved

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