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: $\frac{1}{3}$
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Correct Answer: $\frac{10}{3}$
Solution : Given, $\mathrm{A}=\cot 30° \tan 60°+\cot 60° \tan 30°$ Putting values, we get, $=\sqrt3×\sqrt3+\frac{1}{\sqrt3}×\frac{1}{\sqrt3}$ $=3+\frac{1}{3}$ $=\frac{10}{3}$ Hence, the correct answer is $\frac{10}{3}$.
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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 : If $\frac{x-x\tan^{2}30^{\circ}}{1+\tan^{2}30^{\circ}}=\sin^{2}30^{\circ}+4\cot^{2}45^{\circ}-\sec^{2}60^{\circ}$, then value of $x$ is:
Option 1: $\frac{1}{4}$
Option 2: $\frac{1}{5}$
Option 3: $\frac{1}{2}$
Option 4: $\frac{1}{\sqrt3}$
Question : Find the value of $\cos 0^{\circ}+\cos 30^{\circ}-\tan 45^{\circ}+\operatorname{cosec} 60^{\circ}+\cot 90^{\circ}$.
Option 1: $\frac{7}{6 \sqrt{3}}$
Option 2: $\frac{\sqrt{3}}{6}$
Option 3: $\frac{7}{6}$
Option 4: $\frac{7}{2 \sqrt{3}}$
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 : If $\sqrt{3} \tan ^2 \theta-4 \tan \theta+\sqrt{3}=0$, then what is the value of $\tan ^2 \theta+\cot ^2 \theta$?
Option 1: $\frac{4}{3}$
Option 4: $\frac{6}{5}$
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