1
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
2
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
$$\frac{-16}{65}$$
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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