Question : If $\sin 2A = \cos 15^{\circ}$, then the smallest positive value of A is:

Option 1: 75$^{\circ}$

Option 2: 37.5$^{\circ}$

Option 3: 7.5$^{\circ}$

Option 4: 47.5$^{\circ}$

Question : Find the value of $\frac{\cos 65^{\circ}}{\sin 25^{\circ}}+\frac{5 \sin 19^{\circ}}{\cos 71^{\circ}}-\frac{3 \cos 28^{\circ}}{\sin 62^{\circ}}$.

Option 1: 2

Option 2: 0

Option 3: 1

Option 4: 3

Question : Find the value of $\frac{\sin ^2 39^{\circ}+\sin ^2\left(90^{\circ}–39^{\circ}\right)}{\cos ^2 35^{\circ}+\cos ^2\left(90^{\circ}–35^{\circ}\right)}+3 \tan 25^{\circ} \tan 75^{\circ}$:

Option 1: 2

Option 2: 4

Option 3: 3

Option 4: 1

Question : The value of $\frac{\sin ^2 52^{\circ}+2+\sin ^2 38^{\circ}}{4 \cos ^2 43^{\circ}-5+4 \cos ^2 47^{\circ}}$ is:

Option 1: $3$

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

Option 3: $-\frac{1}{3}$

Option 4: $-3$

Question : Simplify.
$\cos \left(36^{\circ}-\mathrm{A}\right) \cos \left(36^{\circ}+\mathrm{A}\right)+\cos \left(54^{\circ}-\mathrm{A}\right) \cos \left(54^{\circ}+\mathrm{A}\right)$

Option 1: $\cos A$

Option 2: $\sin 2A$

Option 3: $\cos 2A$

Option 4: $\sin A$

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