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

$$ \left(\cos \frac{\pi}{12}-\sin \frac{\pi}{12}\right)\left(\tan \frac{\pi}{12}+\cot \frac{\pi}{12}\right)= $$

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