Question : If $\sin A+\sin ^2 A=1$, then the value of $\cos ^4 A+\cos ^6 A$ is:

Option 1: $\cos A$

Option 2: $\sin A$

Option 3: 1

Option 4: 0

Question : If $1 + \sin^2 θ - 3\sinθ \cosθ = 0$, then the value of $\cotθ$ is:

Option 1: $0$

Option 2: $2$

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

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

Question : If $\frac{2 \sin A-\cos A}{\sin A+\cos A}=1$, then find the value of $\cot A$.

Option 1: $1$

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

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

Option 4: $2$

Question : If $\sin^4\theta+\cos^4\theta=2\sin^2\theta \cos^2\theta$, where $\theta$ is an acute angle, then the value of $\tan\theta$ is:

Option 1: $1$

Option 2: $2$

Option 3: $\sqrt2$

Option 4: $0$

Question : If $\cos \theta+\sec \theta=2$, then the value of $\sin ^6 \theta+\cos ^6 \theta$ is:

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

Option 2: $0$

Option 3: $1$

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