1
COMEDK 2024 Evening Shift
+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
$$\frac{\pi}{3}$$
2
COMEDK 2024 Evening Shift
+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
$$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$$
3
COMEDK 2024 Evening Shift
+1
-0

$$\text { Evaluate: } \cos ^{-1}\left(\cos \frac{35 \pi}{18}\right)-\sin ^{-1}\left(\sin \frac{35 \pi}{18}\right)$$

A
0
B
$$\frac{\pi}{9}$$
C
$$\frac{\pi}{18}$$
D
$$\pi$$
4
COMEDK 2024 Morning Shift
+1
-0

Evaluate : $$\cos ^{-1}\left[\cos \left(-680^{\circ}\right)\right]+\sin ^{-1}\left[\sin \left(-600^{\circ}\right)\right]-\cos ^{-1}\left(\sin 270^{\circ}\right)$$

A
$$\frac{14 \pi}{9}$$
B
$$-\frac{5 \pi}{9}$$
C
$$-\frac{4 \pi}{9}$$
D
$$\pi$$
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