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If $7 \sin^2 A + 3 \cos^2 A = 4$, then find the value of $\tan A$.
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$7 \sin^2 A + 3 \cos^2 A = 4$ ($\frac{1}{2}$ Mark)
$\Rightarrow 7 \sin^2 A + 3(1 - \sin^2 A) = 4$ ($\frac{1}{2}$ Mark)
$\Rightarrow 4 \sin^2 A = 1$ ($\frac{1}{2}$ Mark)
$\Rightarrow \sin A = \frac{1}{2}$ ($\frac{1}{2}$ Mark)
$\Rightarrow A = 30^{\circ}$ ($\frac{1}{2}$ Mark)
$\therefore \tan A = \tan 30^{\circ} = \frac{1}{\sqrt{3}}$ ($\frac{1}{2}$ Mark)
$\Rightarrow 7 \sin^2 A + 3(1 - \sin^2 A) = 4$ ($\frac{1}{2}$ Mark)
$\Rightarrow 4 \sin^2 A = 1$ ($\frac{1}{2}$ Mark)
$\Rightarrow \sin A = \frac{1}{2}$ ($\frac{1}{2}$ Mark)
$\Rightarrow A = 30^{\circ}$ ($\frac{1}{2}$ Mark)
$\therefore \tan A = \tan 30^{\circ} = \frac{1}{\sqrt{3}}$ ($\frac{1}{2}$ Mark)