The greatest and least values of sin x cos x | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $f(x) = \sin x \cos x$. Multiplying and dividing by $2$,we get $f(x) = \frac{2 \sin x \cos x}{2} = \frac{1}{2} \sin(2x)$. We know that the ran

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) Let $f(x) = \sin x \cos x$. Multiplying and dividing by $2$,we get $f(x) = \frac{2 \sin x \cos x}{2} = \frac{1}{2} \sin(2x)$. We know that the range of the sine function is $[-1, 1]$,so $-1 \le \sin(2x) \le 1$. Multiplying the entire inequality by $\frac{1}{2}$,we get $-\frac{1}{2} \le \frac{1}{2} \sin(2x) \le \frac{1}{2}$. Therefore,the greatest value is $\frac{1}{2}$ and the least value is $-\frac{1}{2}$.

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

Similar Questions

$\sin 15^\circ + \cos 105^\circ = $

$\cos \frac{2\pi}{15} \cos \frac{4\pi}{15} \cos \frac{8\pi}{15} \cos \frac{16\pi}{15} = $

If $\alpha + \beta = \frac{\pi}{2}$ and $\beta + \gamma = \alpha$,then $\tan \alpha$ equals

If $a \tan \theta = b$,then $a \cos 2\theta + b \sin 2\theta = $

$\frac{\sin 3\theta + \sin 5\theta + \sin 7\theta + \sin 9\theta}{\cos 3\theta + \cos 5\theta + \cos 7\theta + \cos 9\theta} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module