Question

The greatest and least value of $\sin x\cos x$ are

• A. $1, - 1$
• B. $\frac{1}{2}, - \frac{1}{2}$
• C. $\frac{1}{4}, - \frac{1}{4}$
• D. $2, - 2$

Answer 1

Answer: (B)

$\frac{1}{2}, - \frac{1}{2}$

Answer 2

Let $f(x) = \sin x\cos x = \frac{1}{2}\sin 2x$

We know $- 1 \leq \sin 2x \leq 1 \Rightarrow - \frac{1}{2} \leq \frac{1}{2}\sin 2x \leq \frac{1}{2}$

Thus the greatest and least value of $f(x)$ are $\frac{1}{2}$ and $- \frac{1}{2}$

respectively.