Question

The greatest value of sin⁡ x cos⁡ x is : *​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

We know that for any angle $\theta \:$

$- 1 \leqslant \: \sin \theta \: \leqslant 1$

So For any angle $\theta$

The maximum value of

$\sin \theta$

is 1

2.

$2\sin x \cos x = \sin \: 2x$

TO DETERMINE

The greatest value of $\sin x \cos x$

CALCULATION

Here

$\sin x \cos x$

$\displaystyle \: = \frac{1}{2} \times 2 \sin x \cos x$

$\displaystyle \: = \frac{1}{2} \sin 2x$

Now the maximum value of

$\sin 2x \: \: is \: \: 1$

So the greatest value of

$\displaystyle \: \sin x \cos x \: \: \: is \: \: \: \frac{1}{2}$