Question : If $\tan A=\frac{2}{5}$, then find the value of $\frac{\sec ^2 A}{\operatorname{cosec}^2 A}$.

Option 1: $\frac{2}{5}$

Option 2: $\frac{4}{25}$

Option 3: $\frac{9}{25}$

Option 4: $\frac{3}{5}$

Question : The speeds of two bodies are in the ratio 2 : 3. If the difference in the time taken to cover 50 m is 10 sec, then find the difference in their speeds.

Option 1: $\frac{8}{9} \mathrm{~m} / \mathrm{sec}$

Option 2: $\frac{5}{6} \mathrm{~m} / \mathrm{sec}$

Option 3: $\frac{6}{5} \mathrm{~m} / \mathrm{sec}$

Option 4: $\frac{7}{5} \mathrm{~m} / \mathrm{sec}$

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 : Find the value of $\left(\tan ^2 \theta+\tan ^4 \theta\right)$.

Option 1: $\cot ^2 \theta-\tan ^2 \theta$

Option 2: $\ {\sec}^4 \theta-\ {\sec}^2 \theta$

Option 3: $\ {\sec}^4 \theta-\ {\sec}^4 \theta$

Option 4: $ \ {\sec}^4 \theta+\ {\sec}^2 \theta$

Question : If $\frac{1}{\operatorname{cosec} \theta+1}+\frac{1}{\operatorname{cosec} \theta-1}=2 \sec \theta, 0^{\circ}<\theta<90^{\circ}$, then the value of $\frac{\tan \theta+2 \sec \theta}{\operatorname{cosec} \theta}$ is:

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

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

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

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