Day 52: CBSE Class 12 Maths

1. A.
   $\tan^{-1} (\sin x) + C$
2. B.
   $\sin^{-1} (\sin x) + C$
3. C.
   $\log |\sin x + \sqrt{1 + \sin^2 x}\,| + C$
4. D.
   $\log |\sin x - \sqrt{\sin^2 x + 1}\,| + C$

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1. A.
   $[-1, 1]$
2. B.
   $[-3, 5]$
3. C.
   $[-4, 4]$
4. D.
   $\left[-\dfrac{1}{2}, 0\right]$

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1. A.
   $y = \sec^{-1} x$
2. B.
   $y = \cot^{-1} x$
3. C.
   $y = \tan^{-1} x$
4. D.
   $y = \operatorname{cosec}^{-1} x$

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1. A.
   $-\frac{\pi}{2} < y < \frac{\pi}{2}$
2. B.
   $-\frac{3\pi}{2} < y < \frac{3\pi}{2}$
3. C.
   $-\frac{\pi}{6} < y < \frac{\pi}{6}$
4. D.
   $-\frac{\pi}{6} \leq y \leq \frac{\pi}{6}$

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