Question : If $4-2 \sin ^2 \theta-5 \cos \theta=0,0^{\circ}<\theta<90^{\circ}$, then the value of $\cos \theta-\tan \theta$ is:

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

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

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

Option 4: $\frac{1-2 \sqrt{3}}{2}$

Question : If $4-2 \sin ^2 \theta-5 \cos \theta=0,0^{\circ}<\theta<90^{\circ}$, then the value of $\cos \theta+\tan \theta$ is:

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

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

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

Option 4: $\frac{1-2 \sqrt{3}}{2}$

Question : In a triangle ABC, if $\angle B=90^{\circ}, \angle C=45^{\circ}$ and AC = 4 cm, then the value of BC is:

Option 1: $\sqrt{2} \mathrm{~cm}$

Option 2: $4 \mathrm{~cm}$

Option 3: $2 \sqrt{2} \mathrm{~cm}$

Option 4: $4 \sqrt{2} \mathrm{~cm}$

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

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