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Q. The greatest and least value of sin x cos x are

Trigonometric Functions

Solution:

Let $f\left(x\right) = sin \,x \,cos \, x = \frac{1}{2} \,sin \, 2x$
We know $-1\le \,sin \,2x \le 1 \Rightarrow - \frac{1}{2} \le \frac{1}{2} \, sin \,2x \le \frac{1}{2}$
Thus the greatest and least value of of $f\left(x\right)$ are
$\frac{1}{2}$ and $-\frac{1}{2}$ respectively