Question : If $\sec \theta+\frac{1}{\cos \theta}=2$, find the value of $\sec ^{55} \theta+\frac{1}{\sec ^{55} \theta}$.

Option 1: 2

Option 2: 0

Option 3: 1

Option 4: 55

Question : If $\sec\theta-\cos\theta=\frac{3}{2}$, where $\theta$ is a positive acute angle, then the value of $\sec\theta$ is:

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

Option 2: $1$

Option 3: $2$

Option 4: $0$

Question : $\frac{\sin ^2 \theta}{\cos \theta(1+\cos \theta)}+\frac{1+\cos \theta}{\cos \theta}=$?

Option 1: $\operatorname{cosec}\theta$

Option 2: $\sec\theta$

Option 3: $2\cos\theta$

Option 4: $2\sec\theta$

Question : If $\sin \theta-\cos \theta=0$, then find the value of $\left(\sin^3 \theta-\cos^3 \theta\right)$.

Option 1: $0$

Option 2: $2$

Option 3: $1$

Option 4: $\frac{1}{\sqrt{2}}$

Question : Value of $\sec^2\theta-\frac{\sin^2\theta-2\sin^4\theta}{2\cos^4\theta-\cos^2\theta}$ is:

Option 1: 1

Option 2: 2

Option 3: –1

Option 4: 0

Question : $ \sqrt{\frac{1+\cos \theta}{1-\cos \theta}}+\sqrt{\frac{1-\cos \theta}{1+\cos \theta}}=$________.

Option 1: $2 \sin \theta$

Option 2: $2 \cos \theta$

Option 3: $ 2 \operatorname{cosec} \theta $

Option 4: $2 \sec \theta$