Question : The value of $\cot41°.\cot42°.\cot43°.\cot44°.\cot45°.\cot46°.\cot47°.\cot48°.\cot49°$ is:

Option 1: $1$

Option 2: $0$

Option 3: $\frac{\sqrt3}{2}$

Option 4: $\frac{1}{\sqrt2}$

Question : Simplify the following.
$\cot13° \cot27° \cot45° \cot63° \cot77° = ?$

Option 1: $1$

Option 2: $\sqrt3$

Option 3: $2$

Option 4: $\sqrt2$

Question : If $x=\sqrt{\frac{2+\sqrt3}{2-\sqrt3}}$, then what is the value of $(x^{2}+x-9)$?

Option 1: 0

Option 2: $3\sqrt2$

Option 3: $3\sqrt3$

Option 4: $5\sqrt3$

Question : If $7\sin^2\ \theta+3\cos^2\ \theta=4, (0°<\theta<90°)$, then find the value of $\tan\theta$:

Option 1: $\frac{1}{\sqrt3}$

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

Option 3: $1$

Option 4: $\sqrt3$

Question : If $\sec\theta-\tan\theta=\frac{1}{\sqrt3}$, then the value of $\sec\theta.\tan\theta$ is:

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

Option 2: $\frac{2}{\sqrt3}$

Option 3: $\frac{4}{\sqrt3}$

Option 4: $\frac{1}{\sqrt3}$

Question : If $x=\sqrt2+1$, then the value of $x^{4}-\frac{1}{x^{4}}$ is:

Option 1: $8\sqrt2$

Option 2: $18\sqrt2$

Option 3: $6\sqrt2$

Option 4: $24\sqrt2$