PYQ Vault
EbooksTutor

Simplify sqrt(1+x^2)[{x cos(cot^-1 x) + sin(cot^-1 x)}^2 - 1]^(1/2) for 0 < x < 1

The same question, asked 2 times: 3 May 2023 S2, 15 May 2023 S2. Every wording 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

    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.