Question

M114) solve
cos (2x) = √2 - cos (2x)

Answer 1

To solve the equation cos (2x) = √2 - cos (2x), we can first isolate the variable on one side of the equation.

cos (2x) = √2 - cos (2x)

add cos(2x) to both sides

2*cos(2x) = √2

divide both sides by 2

cos(2x) = √2/2

Now we can use the identity cos 2x = 2cos^2 x - 1, so

2cos^2 x - 1 = √2/2

Square both sides

4cos^2 x - 2 = 2 - 1

4cos^2 x = 1

Divide both sides by 4

cos^2 x = 1/4

Since cos^2 x = 1/4, then cos x = +/- √(1/4) = +/- 1/2

So x = pi/3 + 2npi or x = 5pi/3 + 2n*pi