Question : Simplify the given equation: $\frac{\cot^3A–1}{\cot A–1}$

Option 1: $\operatorname{cosec}^2 \mathrm{A}-\cot \mathrm{A}$

Option 2: $\operatorname{cosec}^2 A+\cot A$

Option 3: $\cot ^2 \mathrm{A}+\operatorname{cosec} \mathrm{A}$

Option 4: $\cot ^2 \mathrm{A}-\operatorname{cosec} \mathrm{A}$

Question : Simplify the given expression.
$\sqrt{\frac{1+\cos P}{1-\cos P}}$

Option 1: $\operatorname{cosec}P-\cot P$

Option 2: $\sec P-\tan P$

Option 3: $\sec P+\tan P$

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

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 : The given expression is equal to:
$1-\frac{\tan ^2 \phi}{\sec ^2 \phi}$

Option 1: $\operatorname{sin}^2 \phi\cos ^2 \phi$

Option 2: $\operatorname{sin}^2 \phi\cot ^2 \phi$

Option 3: $\cot^2 \phi \cos^2 \phi$

Option 4: $\tan^2 \phi\cos^2 \phi$

Question : The value of $\frac{1+\sin A}{\cos A}+\frac{\cos A}{1+\sin A}$ is:

Option 1: $2 \sec A$

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

Option 3: $ \sec A$

Option 4: $ \operatorname{cosec} A$