Question

The greatest and least value of $\sin \theta \cos \theta$ are -

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

Answer 1

The correct option is C $\frac{1}{2},-\frac{1}{2}$

let, $y=\sin \theta .\cos \theta =\frac{2}{2}\sin \theta \cos \theta =\frac{1}{2}\sin 2\theta$
we know, $-1\le \sin 2\theta \le 1\Rightarrow -\frac{1}{2}\le \frac{1}{2}\sin 2\theta \le \frac{1}{2}$
Hence, $y\in [-\frac{1}{2},\frac{1}{2}]$