The value of ^(-1) ( ( ^(-1) 1/2 ) ) + ^(-1)(1) Option 1: ()/6 Option 2: ()/3 Option 3: ()/2 Option 4: (5)/12

Answer: (5)/12. Solution: ^(-1)(1/2) = ()/3. (()/3) = √3/2. ^(-1)(√3/2) = ()/6. ^(-1)(1) = ()/4. Sum: ()/6 + ()/4 = (2 + 3)/12 = (5)/12.

Geometry

Trigonometry

Medium

The value of $\cos^{-1} \left( \sin \left( \cos^{-1} \frac{1}{2} \right) \right) + \tan^{-1}(1)$

$\frac{\pi}{6}$

$\frac{\pi}{3}$

$\frac{\pi}{2}$

$\frac{5\pi}{12}$

✅ Correct Option: 4

$\cos^{-1}(\frac{1}{2}) = \frac{\pi}{3}$ .

$\sin(\frac{\pi}{3}) = \frac{\sqrt{3}}{2}$ .

$\cos^{-1}(\frac{\sqrt{3}}{2}) = \frac{\pi}{6}$ .

$\tan^{-1}(1) = \frac{\pi}{4}$ .

Sum: $\frac{\pi}{6} + \frac{\pi}{4} = \frac{2\pi + 3\pi}{12} = \frac{5\pi}{12}$ .

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Which one of the following is TRUE?

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The graph of $\sin^{-1} x$ is represented by:

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Match List-I with List-II

List-I	List-II
Inverse Trigonometric function	Principal values of arguments
(A) $sin^{-1}\left(\frac{-1}{2}\right)$	(I) $\frac{-\pi}{3}$
(B) $cos^{-1}\left(\frac{-1}{2}\right)$	(II) $\frac{3\pi}{4}$
(C) $tan^{-1}(-\sqrt{3})$	(III) $\frac{-\pi}{6}$
(D) $sec^{-1}(-\sqrt{2})$	(IV) $\frac{2\pi}{3}$

Choose the correct answer from the options given below: