Question : If $0^{\circ}< \theta< 90^{\circ}$ and $\operatorname{cosec \theta} =\cot^{2}\theta$, then the value of expression $\operatorname{cosec^{4}\theta}–\operatorname{2cosec^{2}\theta}-\cot^{2}\theta$ is equal to:

Option 1: $2$

Option 2: $0$

Option 3: $1$

Option 4: $3$

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

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: –2

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 $\frac{\cot \theta+\operatorname{cosec} \theta-1}{\cot \theta-\operatorname{cosec} \theta+1}$?

Option 1: $2 \sec \theta$

Option 2: $2 \operatorname{cosec} \theta$

Option 3: $2 \cot \theta$

Option 4: $\operatorname{cosec} \theta+\cot \theta$

Question : Find the value of $\cos 0^{\circ}+\cos 30^{\circ}-\tan 45^{\circ}+\operatorname{cosec} 60^{\circ}+\cot 90^{\circ}$.

Option 1: $\frac{7}{6 \sqrt{3}}$

Option 2: $\frac{\sqrt{3}}{6}$

Option 3: $\frac{7}{6}$

Option 4: $\frac{7}{2 \sqrt{3}}$