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CUET Mathematics 2022 PYQs25 May Shift 1. Free, no login required.

Geometry

past year questions, CUET Mathematics 2022 25 May Shift 1

Trigonometry

past year questions, Geometry, CUET Mathematics 2022 25 May Shift 1

Easy

core

Value of esin⁡(tan⁡−1x+cot⁡−1x)esin⁡(sin⁡−1x+cos⁡−1x),x∈[−1,1]\frac{e^{\sin(\tan^{-1} x + \cot^{-1} x)}}{e^{\sin(\sin^{-1} x + \cos^{-1} x)}}, x \in [-1, 1], is:

Solution

✅ Correct Option: 3

tan⁡−1x+cot⁡−1x=π2\tan^{-1}x + \cot^{-1}x = \frac{\pi}{2} and sin⁡−1x+cos⁡−1x=π2\sin^{-1}x + \cos^{-1}x = \frac{\pi}{2}. Both numerator and denominator equal esin⁡(π/2)=ee^{\sin(\pi/2)} = e. The ratio is 11.

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The value of sin⁡[π2−sin⁡−1(−32)]\sin\left[\frac{\pi}{2} - \sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right] is :

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Match List-I with List-II

List-I (Functions)List-II (Range, principal value)
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(D) sec⁡−1x\sec^{-1}x(IV) (−π2,π2)\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)

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2022: 10 Aug Shift 1

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cos⁡[tan⁡−1{sin⁡(cot⁡−1x)}]\cos[\tan^{-1}\{\sin(\cot^{-1}x)\}] is equal to

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Match the LIST-I with LIST-II

LIST-I FunctionsLIST-II Principal value
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B. sin⁡−1(−12)\sin^{-1}\left(-\dfrac{1}{\sqrt{2}}\right)II. π6\dfrac{\pi}{6}
C. tan⁡−1(1)\tan^{-1}(1)III. −π4-\dfrac{\pi}{4}
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