Question : If $\tan\left ( A-B \right )=x$, then the value of $x$ is:

Option 1: $\frac{\tan A+\tan B}{1-\tan A \tan B}$

Option 2: $\frac{\tan A+\tan B}{1+\tan A \tan B}$

Option 3: $\frac{\tan A-\tan B}{1-\tan A \tan B}$

Option 4: $\frac{\tan A-\tan B}{1+\tan A \tan B}$

Question : If $A=60^{\circ}$ and $B=30^{\circ}$, find the value of $\frac{(\tan A-\tan B)}{(1+\tan A \tan B)}$.

Option 1: $3$

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

Option 3: $\sqrt{3}$

Option 4: $1$

Question : The given expression is equal to:
$\frac{\left(1+\tan^2 A\right)}{\operatorname{cosec}^2 A \cdot \tan A}$

Option 1: $\sec^2A$

Option 2: $\sec A$

Option 3: $\tan A$

Option 4: $\tan^2A$

Question : If $A=30^{\circ}$, then find the value of $\frac{(2 \tan A)}{\left(1-\tan^2 A\right)}$.

Option 1: $4 \sqrt{3}$

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

Option 3: $3$

Option 4: $2 \sqrt{3}$

Question : What is the value of $3 \tan 20° \tan 45°\tan 70°$?

Option 1: 2

Option 2: 3

Option 3: 1.5

Option 4: 4