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,
Hypotenuse
2
= Perpendicular
2
+ Base
2
Perpendicular = 3 and Base = 1
⇒ Hypotenuse
2
= 3
2
+ 1
2
⇒ Hypotenuse
2
= 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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