1
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } \frac{\cos x}{\cos (x-2 y)}=\lambda \text { then } \tan (x-y) \tan y= $$

A
$$\frac{1+\lambda}{1-\lambda}$$
B
$$\frac{1-\lambda}{1+\lambda}$$
C
$$\frac{\lambda}{1-\lambda}$$
D
$$\frac{\lambda}{1+\lambda}$$
2
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+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
$$2 \sin \theta$$
3
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+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
$$-\frac{(1-\sqrt{3})}{2 \sqrt{2}}$$
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$\cos \theta=\frac{1}{2}\left(x+\frac{1}{x}\right)$$ then $$\frac{1}{2}\left(x^2+\frac{1}{x^2}\right)=$$

A
$$\sin ^2 \theta-\cos ^2 \theta$$
B
$$2\left(\cos ^2 \theta-\sin ^2 \theta\right)$$
C
$$\cos ^2 \theta-\sin ^2 \theta$$
D
$$\frac{1}{2}\left(\sin ^2 \theta-\cos ^2 \theta\right)$$
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