Question : Find the value of $\tan A$, if $\sec A + \tan A = \sqrt{3}$ and $A$ lies between $0^\circ$ and $90^\circ$.

Option 1: $\sqrt{3}$

Option 2: $1$

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

Option 4: $0$

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 : 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 $\mathrm{A}=\cot 30^{\circ} \tan 60^{\circ}+\cot 60^{\circ} \tan 30^{\circ}$, 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: $\frac{1}{3}$

Question : If $\sec x+\cos x=\frac{5}{2}$, where $x$ lies between $0^{\circ}$ and $90^{\circ}$, then what is the value of $\sin ^2 x$ ?

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

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

Option 3: $1$

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