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1
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
$-\frac{2 \pi}{5}$ is the principal value of
A
$\sin ^{-1}\left[\sin \left(\frac{7 \pi}{5}\right)\right]$
B
$\tan ^{-1}\left[\tan \left(\frac{7 \pi}{5}\right)\right]$
C
$\cos ^{-1}\left[\cos \left(\frac{7 \pi}{5}\right)\right]$
D
$\sec ^{-1}\left[\sec \left(\frac{7 \pi}{5}\right)\right]$
2
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The range of $x$ for which the equation $\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)=2 \tan ^{-1} x$ holds true
A
$|x| \leq 1$
B
$\forall x \in R$
C
$x \geq 0$
D
$|x| \geq 1$
3
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { Evaluate: } \cot ^{-1}\left(-\frac{3}{\sqrt{3}}\right)-\sec ^{-1}\left(-\frac{2}{\sqrt{2}}\right)-\operatorname{cosec}^{-1}(-1)-\tan ^{-1}(1) $$

A
$$\frac{\pi}{6}$$
B
$$-\frac{2 \pi}{3}$$
C
0
D
$$\frac{\pi}{3}$$
4
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { The function } f(x)=\tan ^{-1}(\sin x+\cos x) \text { is an increasing function in } $$

A
$$\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$$
B
$$\left(0, \frac{\pi}{2}\right)$$
C
$$\left(-\frac{\pi}{2}, \frac{\pi}{4}\right)$$
D
$$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$$
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