52
MCQ (Single Correct Answer)
If $\sin \theta=\frac{-4}{5}$ and $\theta$ lies in third quadrant, then the value of $\cos \frac{\theta}{2}$ is
A
$\frac{1}{5}$
B
$-\frac{1}{\sqrt{10}}$
C
$-\frac{1}{\sqrt{5}}$
D
$\frac{1}{\sqrt{10}}$
53
MCQ (Single Correct Answer)
The number of solutions of equation $\tan x+\sec x=2 \cos x$ lying in the interval $[0,2 \pi]$ is
A
0
B
1
C
2
D
3
54
MCQ (Single Correct Answer)
The value of $\sin \frac{\pi}{18}+\sin \frac{\pi}{9}+\sin \frac{2 \pi}{9}+\sin \frac{5 \pi}{18}$ is
A
$\sin \frac{7 \pi}{18}+\sin \frac{4 \pi}{9}$
B
1
C
$\cos \frac{\pi}{6}+\cos \frac{3 \pi}{7}$
D
$\cos \frac{\pi}{9}+\sin \frac{\pi}{9}$
55
MCQ (Single Correct Answer)
If $A$ lies in the second quadrant and $3 \tan A+4=0$, then the value of $2 \cot A-5 \cos A+\sin A$ is
A
$\frac{-53}{10}$
B
$\frac{23}{10}$
C
$\frac{37}{10}$
D
$\frac{7}{10}$
56
MCQ (Single Correct Answer)
The value of $\cos ^2 48 \Upsilon-\sin ^2 12 \Upsilon$ is
A
$\frac{\sqrt{5}+1}{8}$
B
$\frac{\sqrt{5}-1}{8}$
C
$\frac{\sqrt{5}+1}{5}$
D
$\frac{\sqrt{5}+1}{2 \sqrt{2}}$