1
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
$$-\frac{(1-\sqrt{3})}{2 \sqrt{2}}$$
2
COMEDK 2024 Morning Shift
+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
$$\frac{1}{2}\left(\sin ^2 \theta-\cos ^2 \theta\right)$$
3
COMEDK 2024 Morning Shift
+1
-0

$$4\left(1+\cos \frac{\pi}{8}\right)\left(1+\cos \frac{3 \pi}{8}\right)\left(1+\cos \frac{5 \pi}{8}\right)\left(1+\cos \frac{7 \pi}{8}\right) \text { is equal to }$$

A
$$\frac{1}{8}$$
B
$$\frac{1}{4}$$
C
$$\frac{1}{2}$$
D
1
4
COMEDK 2024 Morning Shift
+1
-0

$$\text { If } \sin A=\frac{4}{5} \text { and } \cos B=\frac{-12}{13} \text { where } A \text { and } B \text { lie in first and third quadrant respectively. Then } \cos (A+B)=$$

A
$$\frac{16}{65}$$
B
$$\frac{-56}{65}$$
C
$$\frac{56}{65}$$
D
$$\frac{-16}{65}$$
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