If $sin x = 3 cos x$ , then $sin x cos x$ equals

\frac{1}{6}

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\frac{1}{5}

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\frac{2}{9}

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\frac{1}{4}

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\frac{3}{10}

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Solution

The correct option is E $\frac{3}{10}$
Since, $sin x = 3 cos x$
$⟹ tan x = 3$
$∴ sin x = \frac{3}{\sqrt{10}}, c o s x = \frac{1}{\sqrt{10}}$
$⟹ sin x cos x = \frac{3}{\sqrt{10}} \times \frac{1}{\sqrt{10}} = \frac{3}{10}$

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