PYQ Vault
EbooksTutor

Write a trig function of an inverse-trig function algebraically (right-triangle conversion)

This type of question, asked 6 times: 3 May 2023 S2, 4 May 2023 S1, 15 May 2023 S2, 12 May 2024 S1, 12 May 2024 S2, 11 Apr 2026 S2. All 7 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    3 May 2023 S2

    112
    If 0<x<10<x<1, then 1+x2[{xcos⁡(cot⁡−1x)+sin⁡(cot⁡−1x)}2−1]1/2=\sqrt{1+x^{2}}\left[\left\{x\cos\left(\cot^{-1}x\right)+\sin\left(\cot^{-1}x\right)\right\}^{2}-1\right]^{1/2}=

    Tap an option to check your answer.

  2. Question 2

    4 May 2023 S1

    114
    If sin⁡(cot⁡−1(x+1))=cos⁡(tan⁡−1x)\sin(\cot^{-1}(x+1))=\cos(\tan^{-1}x), then considering positive square roots, xx has the value

    Tap an option to check your answer.

  3. Question 3

    15 May 2023 S2

    138
    If 0<x<10 < x < 1, then 1+x2[{xcos⁡(cot⁡−1x)+sin⁡(cot⁡−1x)}2−1]1/2\sqrt{1+x^{2}}\left[\left\{x\cos\left(\cot^{-1}x\right)+\sin\left(\cot^{-1}x\right)\right\}^{2}-1\right]^{1/2} is equal to

    Tap an option to check your answer.

  4. Question 4

    12 May 2024 S1

    115
    If x=cosec(tan⁡−1(cos⁡(cot⁡−1(sec⁡(sin⁡−1a)))))x=\text{cosec}\left(\tan^{-1}\left(\cos\left(\cot^{-1}\left(\sec\left(\sin^{-1}a\right)\right)\right)\right)\right), a∈[0,1]a\in[0,1]

    Tap an option to check your answer.

  5. Question 5

    12 May 2024 S1

    148
    The value of sin⁡(cot⁡−1x)\sin(\cot^{-1}x) is

    Tap an option to check your answer.

  6. Question 6

    12 May 2024 S2

    113
    The value of xx, for which sin⁡ ⁣(cot⁡−1(x))=cos⁡ ⁣(tan⁡−1(1+x))\sin\!\left(\cot^{-1}(x)\right) = \cos\!\left(\tan^{-1}(1+x)\right), is

    Tap an option to check your answer.

  7. Question 7

    11 Apr 2026 S2

    67
    If cot⁡(cos⁡−1x)=sec⁡(tan⁡−1ab2−a2)\cot(\cos^{-1}x) = \sec\left(\tan^{-1}\dfrac{a}{\sqrt{b^2 - a^2}}\right), then the value of xx is

    Tap an option to check your answer.