Question : The value of the expression is:
$\frac{1+2\sin60^{\circ}\cos60^{\circ}}{\sin60^{\circ}+\cos60^{\circ}}+\frac{1-2\sin60^{\circ}\cos60^{\circ}}{\sin60^{\circ}-\cos60^{\circ}}$

Option 1: $2\sqrt{3}$

Option 2: $0$

Option 3: $\sqrt{3}$

Option 4: $2$

Question : Find the value of $\cos 0^{\circ}+\cos 30^{\circ}-\tan 45^{\circ}+\operatorname{cosec} 60^{\circ}+\cot 90^{\circ}$.

Option 1: $\frac{7}{6 \sqrt{3}}$

Option 2: $\frac{\sqrt{3}}{6}$

Option 3: $\frac{7}{6}$

Option 4: $\frac{7}{2 \sqrt{3}}$

Question : If $\sin 2\theta=\frac{\sqrt{3}}{2}$, then the value of $\sin 3\theta$ is equal to $(0^{\circ}\leq \theta\leq 90^{\circ})$:

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

Option 2: $1$

Option 3: $0$

Option 4: $\frac{\sqrt{3}}{2}$

Question : The simplified value of $\frac{3\sqrt 2 }{\sqrt3 + \sqrt6} - \frac{4 \sqrt 3 }{\sqrt{6}+ \sqrt {2}} + \frac{\sqrt 6}{\sqrt{3}+ \sqrt 2}$ is:

Option 1: $\sqrt 2$

Option 2: $\frac{1}{\sqrt2}$

Option 3: $\sqrt 3- \sqrt 2$

Option 4: $0$

Question : The value of the following is:
$\left ( \frac{\sin47^{\circ}}{\cos43^{\circ}} \right )^{2}+\left ( \frac{\cos43^{\circ}}{\sin47^{\circ}} \right )^{2}-4\cos^{2}45^{\circ}$

Option 1: $-1$

Option 2: $0$

Option 3: $1$

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

Question : The value of ($\sin 45^\circ+\cos 45^\circ$) is___________.

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

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

Option 3: $1$

Option 4: ${\sqrt{2}}$