Q. 4 A5.0( 3 Votes )

Differentiate <a

Answer :

Let and v = cos–1x.


We need to differentiate u with respect to v that is find.


We have


By substituting x = cos θ, we have




[ sin2θ + cos2θ = 1]


u = sin–1(sin θ)


(i) Given x ϵ (0, 1)


However, x = cos θ.


cos θ ϵ (0, 1)



Hence, u = sin–1(sin θ) = θ.


u = cos–1x


On differentiating u with respect to x, we get



We know



Now, on differentiating v with respect to x, we get




We have,





Thus,


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