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: $\frac{4}{5}$

Question : If $A+B=90^{\circ}$, then the expression $\frac{\cot A}{\cot B}+\cos ^2 A+\cos ^2 B$ is equal to:

Option 1: $\cot ^2 B$

Option 2: $\operatorname{cosec}^2 A$

Option 3: $\cot ^2 A$

Option 4: $\operatorname{cosec}^2 B$

Question : If $\cot \theta=\frac{1}{\sqrt{3}}, 0^{\circ}<\theta<90^{\circ}$, then the value of $\frac{2-\sin ^2 \theta}{1-\cos ^2 \theta}+\left(\operatorname{cosec}^2 \theta-\sec \theta\right)$ is:

Option 1: 0

Option 2: 2

Option 3: 5

Option 4: 1

Question : If $\cos A=\frac{15}{17}, 0 \leq A \leq 90^{\circ}$, then the value of $\cot(90° - A)$ is:

Option 1: $\frac{8}{15}$

Option 2: $\frac{2 \sqrt{2}}{15}$

Option 3: $\frac{\sqrt{2}}{15}$

Option 4: $\frac{7}{15}$

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