Question : The value of $\sec x - \cos x = $?

Option 1: $\tan x \sin x$

Option 2: $\sec x \tan x$

Option 3: $\tan x \cos x$

Option 4: $\sec x \cos x$

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 $\tan A \tan B+\frac{\cos x}{\cos A \cos B}=1$, then $x=?$

Option 1: $B$

Option 2: $A$

Option 3: $A + B$

Option 4: $A - B$

Question : If $\cos x+\sec x=\frac{7}{2 \sqrt{3}}$, then the value of $\cos ^2 x+\sec ^2 x$ will be_____.

Option 1: $\frac{15}{12}$

Option 2: $\frac{10}{12}$

Option 3: $\frac{25}{10}$

Option 4: $\frac{25}{12}$

Question : If $3 x=\sec A$ and $\frac{3}{x}=\tan A$, then $9\left(x^2-\frac{1}{x^2}\right)$ is:

Option 1: $3$

Option 2: $9$

Option 3: $1$

Option 4: $\frac{1}{9}$