Question

Help with this trigonometric question please? (will give medal & fan)

The value pi/12 is a solution for the equation 2 cos^2 (4x) - 1 = 0

True or false?

Answer 1

If you wanna just give me the answer, that's great, but you don't have to if you don't want to. And explanation/walk through would be just as appreciated

Answer 2

*an

Answer 3

2cos^2 4x - 1 = cos 8x (use trig identity 2cos^2 x - 1 = cos 2x)
cos 8x = 0 = cos Pi/2 = cos 3Pi/2
1. 8x = Pi/2 -> x = Pi/16
2. 8x = 3Pi/2 -> x = 3Pi/16
So, Pi/12 is not a solution.

Answer 4

Thank you! Do you think you could help me with one more true/false question? It's pretty much the same, just with a different value and equation

Answer 5

Go ahead.

Answer 6

There is another way to show that Pi/12 is not a solution. Replace x by Pi/12 in cos 8x.
cos 8x = cos (8Pi/12) = cos (2Pi/3) is not zero.

Answer 7

The value 3pi/2 is a solution for the equation 2 sin^2 x - sin x - 1 = 0

Answer 8

I really appreciate it (:

Answer 9

@thu1935 ?

Answer 10

):

Answer 11

2sin^2 x - sin x - 1 = 0. Call sin x = x. The equation is a quadratic equation:
2x^2 - x - 1= 0. Since a + b + c = 0, then one real root is (1) and the other is (c/a = -1/2), The 2 answers are sin x = 1 and sin x = -1/2.
Since sin (3Pi/2) = -1, then 3Pi/2 is not.......