Solveeit Logo
Login

Question

Question: The minimum value of the function \(2\cos 2x - \cos 4x\) in \(0 \leq x \leq \pi\) is...

The minimum value of the function 2cos⁡2x−cos⁡4x2\cos 2x - \cos 4x in 0≤x≤π0 \leq x \leq \pi is

A

0

B

1

C

32\frac{3}{2}

D

– 3

Answer

– 3

Explanation

Solution

y=2cos⁡2x−cos⁡4xy = 2\cos 2x - \cos 4x = 2cos⁡2x(1−cos⁡2x)+2\cos 2x(1 - \cos 2x) + 1

=4cos⁡2xsin⁡2x+14\cos 2x\sin^{2}x + 1

Obviously, sin⁡2x≥0\sin^{2}x \geq 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.