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 : Which of the following is equal to $\sec A – \cos A$?

Option 1: $\sin A\cot A$

Option 2: $\cot A\ cos A$

Option 3: $\tan  A\sin A$

Option 4: $\cos A\sin A$

Question : What is the value of the expression $\cos 2 A \cos 2 B+\sin ^2(A-B)-\sin ^2(A+B)$?

Option 1: $\sin (2 A-2 B)$

Option 2: $\sin (2 A+2 B)$

Option 3: $\cos (2 A+2 B)$

Option 4: $\cos (2 A-2 B)$

Question : Simplify the following expression.
$\frac{\sin \theta - 2 \sin ^3 \theta}{2 \cos ^3 \theta - \cos \theta}$

Option 1: $\tan \theta$

Option 2: $\sin \theta$

Option 3: $\sec \theta$

Option 4: $\cos \theta$

Question : Find the value of the following expression.
$5\left(\sin ^4 \theta+\cos ^4 \theta\right)+3\left(\sin ^6 \theta+\cos ^6 \theta\right)+19 \sin ^2 \theta \cos ^2 \theta$

Option 1: 8

Option 2: 5

Option 3: 6

Option 4: 7