If cosec θ + cot θ = p, prove that 
.
Given: cosec θ + cot θ = p
p2 – 1 = (cosec θ + cot θ)2 – 1
= cosec2 θ + cot2 θ + 2 cosec θ cot θ – 1
= cosec2 θ – 1 + cot2 θ + 2 cosec θ cot θ
= cot2 θ + cot2 θ + 2 cosec θ cot θ
= 2 cot θ (cot θ + cosec θ)
Also, p2 + 1 = (cosec θ + cot θ)2 + 1
= cosec2 θ + cot2 θ + 2 cosec θ cot θ + 1
= cosec2 θ + 1 + cot2 θ + 2 cosec θ cot θ
= cosec2 θ + cosec2 θ + 2 cosec θ cot θ
= 2 cosec θ (cosec θ + cot θ)
Now, consider L.H.S. = 
= 
= cot θ/cosec θ
= cos θ
= R.H.S.
Hence, proved.
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