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

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

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

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

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

Question : If $3+\cos ^2 \theta=3\left(\cot ^2 \theta+\sin ^2 \theta\right), 0^{\circ}<\theta<90^{\circ}$, then what is the value of $(\cos \theta+2 \sin \theta)$ ?

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

Option 2: $3 \sqrt{2}$

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

Option 4: $\frac{\sqrt{3}+2}{2}$

Question : Find the value of $\sqrt{\frac{1-\tan A}{1+\tan A}}$.

Option 1: $\sqrt{\frac{1+\sin 2 A}{\cos 2 A}}$

Option 2: $\sqrt{\frac{1-\sin 2 A}{\cos 2 A}}$

Option 3: $\sqrt{\frac{1+\sin A}{\cos A}}$

Option 4: $\sqrt{\frac{1-\sin A}{\cos A}}$