Question : If $x=a\sec\theta$ and $y=b\tan\theta$, then $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=?$

Option 1: 1

Option 2: 2

Option 3: 3

Option 4: 4

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

Question : If $x=\frac{2 \sin \theta}{(1+\cos \theta+\sin \theta)}$, then the value of $\frac{1-\cos \theta+\sin \theta}{(1+\sin \theta)}$ is:

Option 1: $\frac{x}{(1+x)}$

Option 2: $x$

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

Option 4: $\frac{(1+x)}{x}$

Question : If $\cos\theta=\frac{3}{5}$, then the value of $\sin\theta.\sec\theta.\tan\theta$ is:

Option 1: $\frac{9}{16}$

Option 2: $\frac{16}{9}$

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

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

Question : If $0\leq \theta\leq \frac{\pi}{2}$ and $\sec^{2}\theta+\tan^{2}\theta=7$, then $\theta$ is:

Option 1: $\frac{5\pi}{12}$

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

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

Option 4: $\frac{\pi}{6}$