Question : The value of $\frac{\sec 54^{\circ}}{\operatorname{cosec} 36^{\circ}}+\frac{\tan 70^{\circ}}{\cot 20^{\circ}}-2 \tan 45^{\circ}$ is equal to:

Option 1: 2

Option 2: 0

Option 3: 1

Option 4: 3

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 : The value of the expression $\left[\operatorname{cot} 1^{\circ} \cdot \operatorname{cot} 2^{\circ} \cdot \operatorname{cot} 3^{\circ} \cdot \operatorname{cot} 4^{\circ} \cdot \operatorname{cot} 5^{\circ} \ldots . \operatorname{cot} 178^{\circ} \cdot \operatorname{cot} 179^{\circ}\right]$ is:

Option 1: $1235$

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

Option 3: $1$

Option 4: $0$

Question : What is the value of $\frac{3 \cos 62^{\circ}}{\sin 28^{\circ}}-\frac{2 \tan 34^{\circ}}{\cot 56^{\circ}} ?$

Option 1: 3

Option 2: 1

Option 3: 5

Option 4: 4

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: $\frac{3}{4}$