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 : 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 : Find the value of $\frac{\cos 37^{\circ}}{\sin 53^{\circ}}-\cos 47^{\circ} \operatorname{cosec} 43^{\circ}$.

Option 1: 0

Option 2: –1

Option 3: 2

Option 4: 1

Question : The value of $\frac{\sin ^2 30^{\circ}+\cos ^2 60^{\circ}+\sec 45^{\circ} × \sin 45^{\circ}}{\sec 60^{\circ}+{\text{cosec}} 30^{\circ}}$ is:

Option 1: $\frac{1}{4}$

Option 2: $-\frac{3}{8}$

Option 3: $\frac{3}{8}$

Option 4: $-\frac{1}{4}$

Question : The value of $\frac{\sin ^2 30^{\circ}+\cos ^2 60^{\circ}-\sec 35^{\circ} \cdot \sin 55^{\circ}}{\sec 60^{\circ}+\operatorname{cosec} 30^{\circ}}$ is equal to:

Option 1: $\frac{1}{8}$

Option 2: $-\frac{1}{4}$

Option 3: $\frac{1}{4}$

Option 4: $-\frac{1}{8}$