Question : $\triangle$XYZ is right angled at Y. If $\angle$X = 60°, then find the value of $(\sec Z+\frac{2}{\sqrt3})$.

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

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

Option 3: $\frac{7}{2\sqrt3}$

Option 4: $\frac{4}{2\sqrt3}$

Question : The value of $\cot 13° \cot 27° \cot 60° \cot 63° \cot 77°$ is:

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

Option 2: $0$

Option 3: $\sqrt{3}$

Option 4: $1$

Question : If $\theta$ is a positive acute angles and $\operatorname{cosec}\theta =\sqrt{3}$, then the value of $\cot \theta -\operatorname{cosec}\theta$ is:

Option 1: $\sqrt2-\sqrt3$

Option 2: $\frac{\sqrt{2}(3+\sqrt{3})}{3}$

Option 3: $\frac{\sqrt{2}(3-\sqrt{3})}{3}$

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

Question : What is the value of $\frac{\cot \theta+\operatorname{cosec} \theta-1}{\cot \theta-\operatorname{cosec} \theta+1}$?

Option 1: $2 \sec \theta$

Option 2: $2 \operatorname{cosec} \theta$

Option 3: $2 \cot \theta$

Option 4: $\operatorname{cosec} \theta+\cot \theta$

Question : The value of $\cos \ 0°+\cos\ 1°+\cos\ 2°......\cos\ 180°$ is:

Option 1: $0$

Option 2: $1$

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

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