Symbiosis National Aptitude Test SNAP 2017 Paper

In the given equation,
1 + $\mathit{s}\mathit{i}{\mathit{n}}^2$ A = 3 sin A cosA
Dividing both sides by $\mathit{c}\mathit{o}{\mathit{s}}^2$ A
We get $\frac{1}{\mathit{c}\mathit{o}{\mathit{s}}^2\mathit{A}}+\frac{\mathit{s}\mathit{i}{\mathit{n}}^2\mathit{A}}{\mathit{c}\mathit{o}{\mathit{s}}^2\mathit{A}}$ = 3 , $\frac{\mathit{s}\mathit{i}\mathit{n}\mathit{A}}{\mathit{c}\mathit{o}\mathit{s}\mathit{A}}$
⇒ $\mathit{s}\mathit{e}{\mathit{c}}^2\mathit{A}+\mathit{t}\mathit{a}{\mathit{n}}^2\mathit{A}$ = 3tanA
$1+\mathit{t}\mathit{a}{\mathit{n}}^2\mathit{A}+\mathit{t}\mathit{a}{\mathit{n}}^2\mathit{A}$ = 3 tan A
⇒ 2tan A - 3 tan A +1 = 0
⇒ $2\mathit{t}\mathit{a}{\mathit{n}}^2\mathit{A}$ - 2 tan A - tan A + 1 = 0
⇒ 2 tan A (tan A - 1) - 1 (tan A - 1) = 0
⇒ (2tan A - 1) (tan A - 1) = 0
⇒ tan A = $\frac{1}{2},1$