Question : If tan A = 3, then what is the value of 3sin A cos A?
Option 1: $\frac{8}{9}$
Option 2: $\frac{9}{10}$
Option 3: $\frac{7}{9}$
Option 4: $\frac{9}{11}$
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Correct Answer: $\frac{9}{10}$
Solution : $\tan A = 3$ $⇒\tan A = \frac{\text{Perpendicular}}{\text{Base}}= \frac{3}{1}$ By Pythagoras Theorem, Hypotenuse2 = Perpendicular2 + Base2 Perpendicular = 3 and Base = 1 ⇒ Hypotenuse2 = 32 + 12 ⇒ Hypotenuse2 = 10 ⇒ Hypotenuse = $\sqrt{10}$ ⇒ cos A = $\frac{\text{Base}}{\text{Hypotenuse}}=\frac{1}{\sqrt{10}}$ ⇒ sin A = $\frac{3}{\sqrt{10}}$ So, 3 sin A cos A $= 3 × \frac{3}{\sqrt{10}}$ × $\frac{1}{\sqrt{10}}=\frac{9}{10}$ Hence, the correct answer is $\frac{9}{10}$.
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