The minimum value of the function 2 2x - 4x in 0 x is - Vidyadip

MCQ

The minimum value of the function $2\cos 2x - \cos 4x$ in $0 \le x \le \pi $ is

A
$0$
B
$1$
C
${3 \over 2}$
✓
$-3$

✓

Answer

Correct option: D.

$-3$

d
(d) $y = 2\cos 2x - \cos 4x$

$ = 2\cos 2x(1 - \cos 2x) + 1 = 4\cos 2x{\sin ^2}x + 1$

Obviously, ${\sin ^2}x \ge 0$

Therefore to be least value of $y,$ $\cos 2x$ should be least $i.e.,$ $ - 1$.

Hence least value of $y$ is $ - \,4 + 1 = - 3$.

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