Answer :


Consider,

(cosecθ + sinθ)(cosecθ - sinθ)

Apply the formula (a2 - b2) = (a+b)(a-b) we get,

(cosecθ + sinθ)(cosecθ - sinθ) = cosec2θ - sin2θ

As we know 1+cot2A = cosec2A
 and 1-cos2A = sin2A

So,

(cosecθ + sinθ)(cosecθ - sinθ) = (1+cot2A) -(1-cos2A )
                                             = 1+cot2A - 1+cos2A
                                              =cot2A +cos2A

Hence Proved.

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