Question : If $\frac{x-x\tan^{2}30^{\circ}}{1+\tan^{2}30^{\circ}}=\sin^{2}30^{\circ}+4\cot^{2}45^{\circ}-\sec^{2}60^{\circ}$, then value of $x$ is:

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

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

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

Option 4: $\frac{1}{\sqrt3}$

Question : If $\sec \beta+\tan \beta=2$, then what is the value of $\cot \beta$?

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

Option 2: $\frac{3}{5}$

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

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

Question : If $6 \sec \theta=10$, then find the value of $\frac{5 \operatorname{cosec} \theta-3 \cot \theta}{4 \cos \theta+3 \sin \theta}$.

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

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

Option 3: $\frac{5}{6}$

Option 4: $\frac{6}{5}$

Question : What is the value of $\frac{1+\tan A}{\operatorname{cosec} A}+\frac{1+\cot A}{\sec A}$?

Option 1: $2\sec^2A$

Option 2: $\sec \mathrm{A} - \mathrm{cosec A}$

Option 3: $\sec \mathrm{A} + \mathrm{cosec A}$

Option 4: $2 \;\mathrm{cosec^2 A}$

Question : If $X$ is 20% less than $Y$, then find the values of$\frac{Y–X}{Y}$ and $\frac{X}{X–Y}$.

Option 1: $\frac{1}{5}$ and $-4$

Option 2: $5$ and $-\frac{1}{4}$

Option 3: $\frac{2}{5}$ and $-\frac{5}{2}$

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