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 $f\left(x\right) = sin \,x \,cos \, x = \frac{1}{2} \,sin \, 2x$ 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