Differentiate with respect to x : cosec-1 ( 1 + x2 / 2x ) The answer: 2 / - Maths - Continuity and Differentiability

Question

Differentiate with respect to x :

cosec-1 ( 1 + x2 / 2x )

The answer: 2 / 1 + x2

Varun.Rawat · Accepted Answer

Let y = cosec-11+ x22xput x = tan θNow, y = cosec-11 + tan2θ2 tan θ⇒y = cosec-1sec2θ2 tan θ⇒y = cosec-112 sin θ cos θ⇒y = cosec-11sin 2θ⇒y = cosec-1cosec 2θ⇒y = 2 θ⇒y = 2 tan-1x⇒dydx = 21+x2