The greatest value of $sin x cos x$ is?

1

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2

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\sqrt{2}

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\frac{1}{2}

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Solution

The correct option is C $\frac{1}{2}$
$sin x cos x = \frac{2 sin x cos x}{2} = \frac{sin 2 x}{2}$ $(∵ sin 2 x = 2 sin x cos x)$
As we know that
$sin 2 x \in [- 1, 1]$
So $\frac{sin 2 x}{2} \in [- \frac{1}{2}, \frac{1}{2}]$
The greatest value of $sin x cos x$ is $\frac{1}{2}$

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