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

Question : Which of the following is the value of $\sqrt{\frac{1-\sin 45^{\circ}}{1+\sin 45^{\circ}}}$?

Option 1: $\cos 45^{\circ} - \tan 45^{\circ}$

Option 2: $\tan 45^{\circ} - \sec 45^{\circ}$

Option 3: $\tan 45^{\circ}$

Option 4: $\sec 45^{\circ} - \tan 45^{\circ}$

Question : If $k\left(\tan 45^{\circ} \sin 60^{\circ}\right)=\cos 60^{\circ} \cot 30^{\circ}$, then the value of k is:

Option 1: $1$

Option 2: $2$

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

Option 4: $\sqrt{3}$

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 : 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: $-3$