Question : What is the value of the expression: $\sin A(1+\frac{\sin A}{\cos A})+\cos A(1+\frac{\cos A}{\sin A})$?

Option 1: $\sec A+\operatorname{cosec}A$

Option 2: $\sin \mathrm{A}+\cos \mathrm{A}$

Option 3: $\sin \mathrm{A}-\cos \mathrm{A}$

Option 4: $\sec \mathrm{A}-\operatorname{cosec} \mathrm{A}$

Question : Find the value of $\frac{\cos A}{1+\sin A}+\frac{1+\sin A}{\cos A}+2$.

Option 1: $1+2 \sec A$

Option 2: $2-\sec A$

Option 3: $2+\sec A$

Option 4: $2(1+\sec A)$

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 : 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 : Find the value of the following expression $\frac{(1+\sec\phi)}{\sec\phi}(1-\cos\phi)$.

Option 1: $\cos ^2 \phi$

Option 2: $\sec ^2 \phi$

Option 3: $\cot ^2 \phi$

Option 4: $\sin ^2 \phi$