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Definition of Functions

For what valu...

Question

For what value of x is the function sin x cos x a maximum?

2 π

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\frac{3 π}{4}

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\frac{π}{2}

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\frac{2 π}{3}

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\frac{π}{4}

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Solution

The correct option is E $\frac{π}{4}$
Let $y = sin x \cdot cos x$
Multiplying and dividing R.H.S. by $2$
$\Rightarrow y = \frac{1}{2} 2 sin x \cdot cos x$
$\Rightarrow y = \frac{sin 2 x}{2}$
now for maximum value of y
$sin 2 x = 1$
$\Rightarrow 2 x = (4 x + 1) \frac{π}{2} [n E Z]$ ,
$\Rightarrow x = (4 n + 1) \frac{π}{4}$
at $n = 0$ we get $x = \frac{π}{4}$ (E).

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