Prove each of the following identities:
Consider L.H.S. = 
Multiply and divide by (cosec θ + cot θ):
= 
= 
= (cosec θ + cot θ)2
Thus, proved.
Also, consider (cosec θ + cot θ)2 = cosec2 θ + cot2 θ+ 2 cosec θ cot θ
= 1 + cot2 θ + cot2 θ+ 2 cosec θ cot θ (∵ 1 + cot2 θ = cosec2 θ)
= (1 + 2 cot2 θ + 2 cosec θ cot θ)
= R.H.S.
Hence, proved.
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