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 : What is the value of $\frac{\tan 45^{\circ}-\tan 15^{\circ}}{1+\tan 45^{\circ} \tan 15^{\circ}}$?

Option 1: $\sqrt{3}$

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

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

Option 4: ${\sqrt{2}}$

Question : The value of $\cos^{2}30^{\circ}+\sin^{2}60^{\circ}+\tan^{2}45^{\circ}+\sec^{2}60^{\circ}+\cos0^{\circ}$ is:

Option 1: $4\frac{1}{2}$

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

Option 3: $6\frac{1}{2}$

Option 4: $7\frac{1}{2}$

Question : Find the value of $\tan 27^{\circ} \tan 34^{\circ}+\tan 34^{\circ} \tan 29^{\circ}+\tan 29^{\circ} \tan 27^{\circ}$.

Option 1: $0$

Option 2: $–1$

Option 3: $\sqrt3$

Option 4: $1$

Question : If ${\operatorname{cosec} 39^{\circ}} = x$, then the value of $ \frac{1}{\operatorname{cosec}^2 51^{\circ}} +\sin^239^{\circ} +\tan ^251^{\circ} -\frac{1}{\sin ^2 51^{\circ} \sec ^2 39^{\circ}}$ is:

Option 1: $x^2-1$

Option 2: $\sqrt{x^2-1}$

Option 3: $ \sqrt{1-x^2}$

Option 4: $1-x^2$