Question : If $\cos A=\frac{1}{2}, 0 \leq A \leq 90^{\circ}$, then what is the value of sin (180 - A)?

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

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

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

Option 4: $1$

Question : If $\operatorname{cosec} A+\cot A=3$, $0 \leq A \leq 90^{\circ}$, then find the value of cos A.

Option 1: $\frac{3}{4}$

Option 2: $\frac{2}{5}$

Option 3: $\frac{3}{5}$

Option 4: $\frac{4}{5}$

Question : If $3+\cos ^2 \theta=3\left(\cot ^2 \theta+\sin ^2 \theta\right), 0^{\circ}<\theta<90^{\circ}$, then what is the value of $(\cos \theta+2 \sin \theta)$ ?

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

Option 2: $3 \sqrt{2}$

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

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

Question : If $\sin A=\frac{\sqrt{3}}{2}, 0<A<90^{\circ}$, then find the value of $2(\operatorname{cosec} A + \cot A)$.

Option 1: $2 \sqrt{3}$

Option 2: $\sqrt{3}$

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

Option 4: $\frac{1}{\sqrt{3}}$

Question : If $\tan A=\frac{4}{3}, 0 \leq A \leq 90^{\circ}$, then find the value of $\sin A$.

Option 1: $\frac{3}{5}$

Option 2: $1$

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

Option 4: $\frac{4}{5}$