The greatest and least value of sin x cos x are

Question

The greatest and least value of sin x cos x are (A) 1 , - 1 (B) (1/2) ,-(1/2)  (C) (1/4) ,-(1/4)  (D) 2, - 2

Tardigrade Admin · Accepted Answer

Let f(x) = sin x cos x = (1/2) sin 2x We know -1 le sin 2x le 1 ⇒ - (1/2) le (1/2) sin 2x le (1/2) Thus the greatest and least value of of f(x) are (1/2) and -(1/2) respectively

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

$1, - 1$

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

$\frac{1}{4}, - \frac{1}{4}$

$2, - 2$

Let $f (x) = s in x cos x = \frac{1}{2} s in 2 x$
We know $- 1 \leq s in 2 x \leq 1 \Rightarrow - \frac{1}{2} \leq \frac{1}{2} s in 2 x \leq \frac{1}{2}$
Thus the greatest and least value of of $f (x)$ are
$\frac{1}{2}$ and $- \frac{1}{2}$ respectively

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

1,−1

21​,−21​

41​,−41​

2,−2

Let f(x)=sinxcosx=21​sin2x We know −1≤sin2x≤1⇒−21​≤21​sin2x≤21​ Thus the greatest and least value of of f(x) are 21​ and −21​ respectively

$1, - 1$

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

$\frac{1}{4}, - \frac{1}{4}$

$2, - 2$

Let $f (x) = s in x cos x = \frac{1}{2} s in 2 x$
We know $- 1 \leq s in 2 x \leq 1 \Rightarrow - \frac{1}{2} \leq \frac{1}{2} s in 2 x \leq \frac{1}{2}$
Thus the greatest and least value of of $f (x)$ are
$\frac{1}{2}$ and $- \frac{1}{2}$ respectively