Question : If $\sec A=\frac{9}{4}$, then what is the value of $\cot A$?

Option 1: $\frac{4}{\sqrt{65}}$

Option 2: $\frac{9}{\sqrt{65}}$

Option 3: $\frac{\sqrt{65}}{9}$

Option 4: $\frac{\sqrt{65}}{4}$

Question : If $\cos^{4}\theta-\sin^{4}\theta=\frac{2}{3}$, then the value of $1-2\sin^{2}\theta$ is:

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

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

Option 3: $1$

Option 4: $0$

Question : If $2x+\frac{1}{4x}=1$, then the value of $x^{2}+\frac{1}{64x^{2}}$ is:

Option 1: $0$

Option 2: $1$

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

Option 4: $2$

Question : If $\frac{\sin \theta-\cos \theta}{\sin \theta+\cos \theta}=\frac{4}{5}$, then the value of $\frac{\operatorname{cosec}^2 \theta}{2-\operatorname{cosec}^2 \theta}$ is:

Option 1: $\frac{16}{25}$

Option 2: $\frac{40}{41}$

Option 3: $\frac{41}{40}$

Option 4: $\frac{31}{30}$

Question : If $a+\frac{1}{a}=2$ and $b+\frac{1}{b}=-2$, then what is the value of $a^2+\frac{1}{a^2}+b^2+\frac{1}{b^2} ?$

Option 1: 0

Option 2: 2

Option 3: 8

Option 4: 4