PYQ Vault
EbooksTutor

y = sin^2 or cos^2 of cot^-1(sqrt((1 - x)/(1 + x))): find dy/dx

The same question, asked 4 times: 10 May 2023 S2*, 21 Apr 2025 S2*, 13 Apr 2026 S2*, 20 Apr 2026 S2. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    10 May 2023 S2

    125
    If y=sin⁡2 ⁣(cot⁡−1 ⁣1+x1−x)y = \sin^2\!\left(\cot^{-1}\!\sqrt{\frac{1+x}{1-x}}\right), then dydx\frac{dy}{dx} has the value

    Tap an option to check your answer.

  2. Question 2

    21 Apr 2025 S2

    114
    If y=sin⁡2(cot⁡−1(1−x1+x))y=\sin^{2}\left( \cot^{- 1}\left( \sqrt{\frac{1 -x}{1 +x}} \right) \right), then dy dx=\frac{dy}{\text{ }dx}=

    Tap an option to check your answer.

  3. Question 3

    13 Apr 2026 S2

    71
    ddx[sin⁡2{cot⁡−11−x1+x}]=…\dfrac{d}{dx}\left[\sin^2\left\{\cot^{-1}\sqrt{\dfrac{1 - x}{1 + x}}\right\}\right] = \ldots

    Tap an option to check your answer.

  4. Question 4

    20 Apr 2026 S2

    71
    If y=cos⁡2[cot⁡−1(1−x1+x)]y = \cos^2\left[\cot^{-1}\left(\sqrt{\dfrac{1 - x}{1 + x}}\right)\right] then dydx=\dfrac{dy}{dx} = ........

    Tap an option to check your answer.