Question : What will be the value of $\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$?

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

Option 2: $\sqrt{3}$

Option 3: $1$

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

Question : The value of $\frac{\left(\cos 9^{\circ}+\sin 81^{\circ}\right)\left(\sec 9^{\circ}+{\operatorname{cosec}} \;81^{\circ}\right)}{{\operatorname{cosec}}^2 \;71^{\circ}+\cos ^2 15^{\circ}-\tan ^2 19^{\circ}+\cos ^2 75^{\circ}} $ is:

Option 1: 1

Option 2: 4

Option 3: 5

Option 4: 2

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

Option 1: $\operatorname{cosec} \theta \sec \theta$

Option 2: $\operatorname{cosec} \theta$

Option 3: $\sin \theta \cos \theta$

Option 4: $\sec \theta$

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 : What is the value of $3 \sin ^2 30^{\circ}+\frac{3}{5} \cos ^2 60^{\circ}–2 \sec ^2 45^{\circ} $?

Option 1: $-\frac{5}{2}$

Option 2: $-\frac{5}{8}$

Option 3: $-\frac{31}{10}$

Option 4: $-\frac{25}{17}$