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,


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