Question : The value of $\tan 5^{\circ} \tan 25^{\circ} \tan 45^{\circ} \tan 65^{\circ} \tan 85^{\circ}$ is ______.

Option 1: 4

Option 2: 3

Option 3: 1

Option 4: 2

Question : The value of $\frac{3\left(\cot ^2 47^{\circ}-\sec ^2 43^{\circ}\right)-2\left(\tan ^2 23^{\circ}-\operatorname{cosec}^2 67^{\circ}\right)}{\operatorname{cosec}^2\left(68^{\circ}+\theta\right)-\tan \left(\theta+61^{\circ}\right)-\tan ^2\left(22^{\circ}-\theta\right)+\cot \left(29^{\circ}-\theta\right)}$ is:

Option 1: –1

Option 2: 1

Option 3: 5

Option 4: 0

Question : What is the value of $\tan 6^{\circ} × \tan 45^{\circ} × \tan 84^{\circ}$?

Option 1: $1$

Option 2: $\tan 6^{\circ} \times \tan 39^{\circ}$

Option 3: $3$

Option 4: $\tan 6^{\circ}+\tan 45^{\circ}+\tan 84^{\circ}$

Question : Find the value of $\tan (–1125°)$.

Option 1: $1$

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

Option 3: $–1$

Option 4: $0$

Question : If $x\sin ^{2}60^{\circ}-\frac{3}{2}\sec 60^{\circ}\tan^{2}30^{\circ}+\frac{4}{5}\sin ^{2}45^{\circ}\tan ^{2}60^{\circ}=0$, then $x$ is:

Option 1: $-\frac{1}{15}$

Option 2: $–4$

Option 3: $-\frac{4}{15}$

Option 4: $–2$