Solve 2cosx - 2sinx + cos2x = 0

[tomix186]

I have problem with this equation:

. . . . .Solve 2cosx - 2sinx + cos2x = 0

I have tried to solve for x but without success, so then I started to randomly type values of x and I found out that it is pi/4 or 45degrees.
But I am wondering if there is a way to solve it using some mathematical relationships or formulas.
Thank you for your time

 

[stapel]

I have problem with this equation:

. . . . .Solve 2cosx - 2sinx + cos2x = 0

I have tried to solve for x but without success...

Please reply showing your work, so we can see what you've tried. For instance, what identities did you apply? And so forth.

When you reply, please confirm that your equation is as follows:

. . . . .\(\displaystyle 2\,\cos(x)\, -\, 2\, \sin(x)\, +\, \cos(2x)\, =\, 0\)

Thank you!