Question : If $2 \frac{\cos ^2 x-\sec ^2 x}{\tan ^2 x}=a+b \cos 2 x$, then $a, b=$?

Option 1: $-\frac{3}{2}, -\frac{1}{2}$

Option 2: $\frac{3}{2}, \frac{1}{2}$

Option 3: $-3, -1$

Option 4: $3,1$

Question : If $\tan \frac{A}{2}=x$, then find $x$.

Option 1: $\frac{\sqrt{1+\cos A}}{\sqrt{1-\cos A}}$

Option 2: $\frac{\sqrt{1-\sin A}}{\sqrt{1+\cos A}}$

Option 3: $\frac{\sqrt{1-\cos A}}{\sqrt{1+\cos A}}$

Option 4: $\frac{\sqrt{\cos A-1}}{\sqrt{1+\cos A}}$

Question : If $x+\frac{1}{x}=2 \cos \theta$, then $x^3+\frac{1}{x^3}=?$

Option 1: $2 \cos 2θ$

Option 2: $\cos 3θ$

Option 3: $2 \cos 3θ$

Option 4: $\cos 2θ$

Question : If $\cos x=-\frac{1}{2}, x$ lies in third quadrant, then $\tan x=?$

Option 1: $\sqrt{3}$

Option 2: $\frac{\sqrt{3}}{2}$

Option 3: $\frac{2}{\sqrt{3}}$

Option 4: $\frac{1}{\sqrt{3}}$

Question : If $\cos \theta=\frac{\sqrt{3}}{2}$, then $\tan ^2 \theta \cos ^2 \theta=?$

Option 1: $\frac{1}{\sqrt{3}}$

Option 2: $\frac{1}{4}$

Option 3: $\frac{1}{2}$

Option 4: $\sqrt{3}$