Question : If $7\sin^2\ \theta+3\cos^2\ \theta=4, (0°<\theta<90°)$, then find the value of $\tan\theta$:

Option 1: $\frac{1}{\sqrt3}$

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

Option 3: $1$

Option 4: $\sqrt3$

Question : $\frac{(1+\sec \theta \operatorname{cosec} \theta)^2(\sec \theta-\tan \theta)^2(1+\sin \theta)}{(\sin \theta+\sec \theta)^2+(\cos \theta+\operatorname{cosec} \theta)^2}, 0^{\circ}<\theta<90^{\circ}$, is equal to:

Option 1: $1-\cos \theta$

Option 2: $1-\sin \theta$

Option 3: $\cos \theta$

Option 4: $\sin \theta$

Question : If $\sin5\theta = \cos 20° (0°<\theta<90°)$, then the value of $\theta$ is:

Option 1: 4°

Option 2: 22°

Option 3: 10°

Option 4: 14°

Question : $\frac{1+\cos \theta-\sin ^2 \theta}{\sin \theta(1+\cos \theta)} \times \frac{\sqrt{\sec ^2 \theta+\operatorname{cosec}^2 \theta}}{\tan \theta+\cot \theta}, 0^{\circ}<\theta<90^{\circ}$, is equal to:

Option 1: $\sin \theta$

Option 2: $\cos \theta$

Option 3: $\operatorname{cosec} \theta$

Option 4: $\cot \theta$

Question : The expression $\frac{(1-\sin \theta+\cos \theta)^2(1-\cos \theta) \sec ^3 \theta\; {\operatorname{cosec}}^2 \theta}{(\sec \theta-\tan \theta)(\tan \theta+\cot \theta)}, 0^{\circ}<\theta<90^{\circ}$, is equal to:

Option 1: $\sin \theta$

Option 2: $2 \cos \theta$

Option 3: $\cot \theta$

Option 4: $2 \tan \theta$