Question : Which of the following options gives an expression equivalent to $\sin \ (A + B)$?

Option 1: $\cos\ A \cos\ B - \sin \ A \sin \ B$

Option 2: $\sin\  A \cos \ B + \cos\ A\ \sin \ B$

Option 3: $\cos \ A \cos\ B+\sin\ A \sin \ B$

Option 4: $\sin \ A \cos \ B - \cos \ A \sin \ B$

Question : Solve the following to find its value in terms of trigonometric ratios.
$(\sin A + \cos A)(1 - \sin A \cos A)$

Option 1: $\sin^3A+\cos^3A$

Option 2: $\sin^2A-\cos^2A$

Option 3: ${[\cos A-\sin A]\left[\sin ^2 A+\cos ^2 A\right]}$

Option 4: $\sin^3A-\cos^3A$

Question : If $\cos A+\sin A=\sqrt{2}\cos A$, then $\cos A-\sin A$ is equal to: (where $0^{\circ}< A< 90^{\circ}$)

Option 1: $\sqrt{2}\sin A$

Option 2: $2\sin A$

Option 3: $2\sqrt{\sin A}$

Option 4: $\sqrt{2\sin A}$