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Question

ddx[sin2cot-11+x1-x]=


A

0

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B

-12

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C

12

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D

-1

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Solution

The correct option is B

-12


Simplifying the function using Trigonometric identities

Given, y=[sin2cot-11+x1-x]

Let,

1+x1-x=cotθ

1+x1-x=cot2θ

x=cot2θ-1cot2θ+1

x=cos2θ-sin2θcos2θ+sin2θ

x=cos2θ

As,

1+x1-x=cotθ

y=sin2θ

dydx=2sinθcosθ×-12sin(2θ)=-12

Hence, Option (B) is the correct answer.


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