Question : What is the value of $\left(\tan 10^{\circ} \tan 80^{\circ}+\tan 20^{\circ} \tan 70^{\circ}+\tan 30^{\circ} \tan 60^{\circ}+\tan 40^{\circ} \tan 50^{\circ}\right)$?

Option 1: 4

Option 2: 3

Option 3: 5

Option 4: 2

Question : If $\tan 2 \theta=\cot \left(\theta-36^{\circ}\right)$, where $2 \theta$ is an acute angle, then the value of $\theta$ is:

Option 1: 18°

Option 2: 36°

Option 3: 30°

Option 4: 42°

Question : Evaluate the given expression: $\cos ^2 36^{\circ}+\cos 54^{\circ} \cdot \sin 36^{\circ}+\left(\frac{\tan 26^{\circ}}{\cot 64^{\circ}}\right)$

Option 1: 4

Option 2: 3

Option 3: 1

Option 4: 2

Question : If $\cot 3 \mathrm{~A}=\tan \left(\mathrm{A}-36^{\circ}\right)$, then what is the value of $\mathrm{A}$?

Option 1: 33.5 degrees

Option 2: 25 degrees

Option 3: 30 degrees

Option 4: 31.5 degrees

Question : If $\mathrm{A}=\cot 30^{\circ} \tan 60^{\circ}+\cot 60^{\circ} \tan 30^{\circ}$, then what is the value of A?

Option 1: $\frac{1}{ \sqrt{ 3}}$

Option 2: $\frac{10}{3}$

Option 3: $\frac{10}{ \sqrt{3}}$

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