Question : What is the value of the following in terms of trigonometric ratios?
$\frac{\sin A}{1+\cos A}+\frac{1+\cos A}{\sin A}$

Option 1: $2\operatorname{cosec A}$

Option 2: $2\operatorname{cos A}$

Option 3: $2\operatorname{sec A}$

Option 4: $2\operatorname{sin A}$

Question : Find the value of $\sin (50^{\circ} + A) – \cos (40^{\circ} - A)$.

Option 1: 2

Option 2: 0

Option 3: –1

Option 4: 1

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 a³ + b³ = 217 and a + b = 7, then the value of ab is:

Option 1: – 6

Option 2: – 1

Option 3: 7

Option 4: 6

Question : If $\sin (A-B)=\sin A \cos B–\cos A\sin B$, then $\sin 15°$ will be:

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

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

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

Option 4: $\frac{\sqrt{3}–1}{2\sqrt{2}}$