1
COMEDK 2024 Evening Shift
+1
-0

$$\sqrt{2+\sqrt{2+\sqrt{2+2 \cos 8 \theta}}} \text { where } \theta \in\left[-\frac{\pi}{8}, \frac{\pi}{8}\right] \text { is equal to }$$

A
$$\sin 2 \theta$$
B
$$2 \cos \theta$$
C
$$\cos 2 \theta$$
D
$$2 \sin \theta$$
2
COMEDK 2024 Evening Shift
+1
-0

$$\text { Value of } \cos 105^{\circ} \text { is }$$

A
$$\frac{(\sqrt{3}+1)}{2 \sqrt{2}}$$
B
$$-\frac{(\sqrt{3}-1)}{2 \sqrt{2}}$$
C
$$-\frac{(\sqrt{3}+1)}{2 \sqrt{2}}$$
D
$$-\frac{(1-\sqrt{3})}{2 \sqrt{2}}$$
3
COMEDK 2023 Morning Shift
+1
-0

If $$\cos A=m \cos B$$ and $$\cot \left(\frac{A+B}{2}\right)=\lambda \tan \left(\frac{B-A}{2}\right)$$, then $$\lambda$$ is equal to

A
$$\frac{m}{m-1}$$
B
$$\frac{m+1}{m}$$
C
$$\frac{m+1}{m-1}$$
D
None of these
4
COMEDK 2023 Morning Shift
+1
-0

The expression $$\frac{2 \tan A}{1-\cot A}+\frac{2 \cot A}{1-\tan A}$$ can be written as

A
$$\sin 2 A+\cos 2 A$$
B
$$2 \sec A \operatorname{cosec} A+2$$
C
$$\tan 2 A+\cot 2 A$$
D
$$\sec 2 A+\operatorname{cosec} 2 A$$
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