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

Option 1: $1$

Option 2: $\sqrt3$

Option 3: $2$

Option 4: $\sqrt2$

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 : 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 : Simplify the following expression.
$(4 x + 1)^2 - (4 x + 3)(4 x - 1)$

Option 1: $(4 x + 1)$

Option 2: $4$

Option 3: $(4x- 3)$

Option 4: $4x$

Question : Evaluate the following.
$\sin 25° \sin 65° – \cos 25° \cos 65°$

Option 1: 4

Option 2: 1

Option 3: 0

Option 4: 40