Answer :

Consider LHS,


LHS =


Multiplying and dividing with (cosecθ - cotθ),


= ×


We know that (a + b) (a – b) = a2 – b2.


=


We know that cosec2θ - cot2θ = 1.


=


We know that = cosecθ and = cotθ.


= sinθ () - sinθ ()


= 1 – cosθ = RHS


Hence proved.


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