Question

What is the ordered pair of positive intgers (a,b) for which a/b is a reduced fraction and \[x = \frac{a \pi}{b}\] is the least positive solution of the equation: \[(2 \cos (8x) - 1)(2 \cos (4x) - 1)(2 \cos (2x) - 1)(2 \cos (x) - 1) = 1\]?

Answer 1

0?

Answer 2

i don't know the solution

Answer 3

\( 2 \pi \) ?

Answer 4

how do you get that?

Answer 5

What course are you taking moneybird that this problem came from?

Answer 6

Grade 10 math

Answer 7

ty

Answer 8

This equation will be true if each factor = 1. Each factor will equal 1 if x = 0. So a/b, which must be 2 positive integers is 2/1

Answer 9

how about 1 factor is 4, and 1 factor is 1/4

Answer 10

That could not be true. The largest value of the cos is 1

Answer 11

So the largest value of 2cos x is 2

Answer 12

The maximum of every parenthetical is 1, the minimum is -2. You would need multiplicative inverses and even factors of positive for this to work

Answer 13

Regardless of the value of x

Answer 14

Let me think about it

Answer 15

good work