Choose the correct answer from the given four options: The maximu… - Vidyadip

MCQ

Choose the correct answer from the given four options:
The maximum value of $\sin\text{x}\cdot\cos\text{x}$ is:

A
$\frac{1}{4}$
✓
$\frac{1}{2}$
C
$\sqrt{2}$
D
$2\sqrt{2}$

✓

Answer

Correct option: B.

$\frac{1}{2}$

$\text{f(x)}=\sin\text{x}\cos\text{x}=\frac{1}{2}\sin2\text{x}$
Clearly maximum value of f(x) is $\frac{1}{2},$ when $\sin2\text{x}=1$

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