cot^3 x + cot x = cot x / 1 - cos^2 x
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Step-by-step explanation:
take LHS.
= cot³x + cotx
= cot²x.cotx + cotx
= cot²x (cosx/sinx) + (cosx/sinx)
= (cosx cot²x + cosx) / sinx
= cosx( cot²x + 1) / sin x
= cosx {(cos²x/sin²x) +1} / sinx
= cosx { (cos²x + sin²x/ sin²x) } / sinx
= cosx (1/ sin³x)
= cosx/ sinx. sin²x
= cotx/ 1- cos²x
= RHS proved.
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