The value of [()/2 - ^(-1)(-√3/2)] is : Option 1: 1/2 Option 2: 1/√2 Option 3: √3/2 Option 4: -√3/2

Answer: 1/2. Solution: ^(-1)(-√3/2) = -()/3. So expression = (()/2+()/3) = (-()/3) = ()/3 = 1/2.

Geometry

Trigonometry

Easy

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

$\frac{1}{2}$

$\frac{1}{\sqrt{2}}$

$\frac{\sqrt{3}}{2}$

$-\frac{\sqrt{3}}{2}$

✅ Correct Option: 1

$\sin^{-1}(-\frac{\sqrt{3}}{2}) = -\frac{\pi}{3}$ . So expression $= \sin(\frac{\pi}{2}+\frac{\pi}{3}) = \cos(-\frac{\pi}{3}) = \cos\frac{\pi}{3} = \frac{1}{2}$ .

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The principal value of $\cot^{-1}\left(\frac{-1}{\sqrt{3}}\right)$ is :

The value of sin⁡[π2−sin⁡−1(−32)]\sin\left[\frac{\pi}{2} - \sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right]sin[2π​−sin−1(−23​​)] is :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

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