Question

Find all solutions to the equation in the interval [0, 2π). cos 2x - cos x = 0

Answer 1

Use the following to make a substitution in your equation:
\[\cos(2x)=2\cos ^{2}(x)-1\]

Answer 2

So would it be 2cos^2(x) -1 cos

Answer 3

That's not the complete equation we get after making the substitution. We now have
\[2\cos^{2}(x)−1-\cos(x)=0\]\[2\cos^{2}(x)-\cos(x)-1=0\]
Now we just think of this as a quadratic....but instead of x we have cos(x). You can factor it just like a quadratic.

Answer 4

how

Answer 5

How would you factor 2a^2 - a -1 ?
(2a + 1)(a -1)
But, instead of a, we have cos(x)

Answer 6

(2cos(x) + 1)(cos(x) -1) = 0
So, just like with normal quadratics, one of those 2 factors must be 0
Either 2cos(x) + 1 = 0 or cos(x) - 1 = 0. Solve both of those equations, and you'll have your answer(s)

Answer 7

Ok thanks