Question : If $\sin\phi=\frac{5}{6}$, the value of $\cot\phi \cdot \sin\phi \cdot \cos\phi$ is:

Option 1: $\frac{6}{5}$

Option 2: $\frac{25}{36}$

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

Option 4: $\frac{11}{36}$

Question : Simplify the given equation: $(1+\tan ^2 A)(1+\cot ^2 A)=?$

Option 1: $\frac{1}{\cos ^2 A\left(1+\sin ^2 A\right)}$

Option 2: $\frac{1}{\sin ^2 A\left(1-\sin ^2 A\right)}$

Option 3: $\frac{1}{\sin ^2 A+\operatorname{cosec}^2 A}$

Option 4: $\frac{1}{\sin ^2 A\left(1+\cos ^2 A\right)}$

Question : What is the value of $\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta}+\frac{\sin \theta-\cos \theta}{\sin \theta+\cos \theta}$?

Option 1: $\frac{1}{\left(\sin ^2 \theta-\cos ^2 \theta\right)}$

Option 2: $2\left(\sin ^2 \theta-\cos ^2 \theta\right)$

Option 3: $\frac{2}{\left(\sin ^2 \theta-\cos ^2 \theta\right)}$

Option 4: $\sin ^2 \theta-\cos ^2 \theta$

Question : If $\operatorname{cosec} A+\cot A=a \sqrt{b}$, then find the value of $\frac{\left(a^2 b-1\right)}{\left(a^2 b+1\right)}$.

Option 1: $\cos A$

Option 2: $\tan A$

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

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

Question : If $\sin A+\sin ^2 A=1$, then the value of the expression $\left(\cos ^2 A+\cos ^4 A\right)$ is

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

Option 2: $1$

Option 3: $2$

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