If y= ²≤ft[ ^{-1}≤ft({1-x/1+x})] then d y/d x=·s ·s.

Correct Answer is : −12-1/22−1

Correct Answer is : −12-1/22−1

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MHTCET 20 Apr 2026 Shift 2 Paper

Question : 121 of 150

Marks: +1, -0

y=\cos ^{2}\left[\cot ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right)\right]

\frac{d y}{d x}=\cdots \cdots

Solution:

Concept:

Use the inverse trigonometric relation and the identity connecting

\cot^2\theta

and

\cos^2\theta

to simplify

y

before differentiating.

Explanation:

Let

\theta = \cot^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right)

Then

\cot \theta = \sqrt{\frac{1-x}{1+x}}

, so

\cot^2 \theta = \frac{1-x}{1+x}

Given

y = \cos^2\theta

, use the identity:

\cos^2 \theta = \frac{\cot^2 \theta}{1 + \cot^2 \theta}

Substitute

\cot^2\theta = \frac{1-x}{1+x}

y = \frac{\frac{1-x}{1+x}}{1+\frac{1-x}{1+x}} = \frac{\frac{1-x}{1+x}}{\frac{2}{1+x}} = \frac{1-x}{2}

Differentiate with respect to

x

\frac{dy}{dx} = \frac{d}{dx}\left(\frac{1-x}{2}\right) = -\frac{1}{2}

Answer:

\frac{dy}{dx} = -\frac{1}{2}

, hence Option A.

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