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
$\frac{\sqrt{5}+1}{2 \sqrt{2}}$
57
MCQ (Single Correct Answer)
If $\tan \alpha=\frac{1}{7}$ and $\tan \beta=\frac{1}{3}$, then $\cos 2 \alpha$ is equal to
A
$\sin 2 \beta$
B
$\sin 4 \beta$
C
$\sin 3 \beta$
D
$\cos 2 \beta$
58
MCQ (Single Correct Answer)
$$ \text { If } \tan \theta=\frac{a}{b} \text {, then } b \cos 2 \theta+a \sin 2 \theta \text { is equal to } $$
A
a
B
b
C
$\frac{a}{b}$
D
None of these
59
MCQ (Single Correct Answer)
If for real values of $x, \cos \theta=x+\frac{1}{x}$, then
A
$\theta$ is an acute angle
B
$\theta$ is right angle
C
$\theta$ is an obtuse angle
D
No value of $\theta$ is possible
60
60 The value of $\frac{\sin 50 \Upsilon}{\sin 130 \Upsilon}$ is .............. .
Explanation
$$\begin{aligned} \text{Here,}\quad \frac{\sin 50 \Upsilon}{\sin 130 \Upsilon} & =\frac{\sin (180 \Upsilon-130 \Upsilon)}{\sin 130 \Upsilon} \\ & =\frac{\sin 130 \Upsilon}{\sin 130 \Upsilon}=1 \end{aligned} $$