SOLUTION: Please solve the equation for the interval [ 0, 2pi ]: {{{2cos^2(2x)-cos(2x)=0}}} Thank you!

Question 983734: Please solve the equation for the interval [ 0, 2pi ]:

Thank you!
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!

One solution is

= .

It gives    = , where    is an arbitrary integer (k = 0, +/-1, +/-2, . . . ).

Hence = .

It gives for k = 0, 1, 2, 3

= , = , = , = .

Next, if is not zero, then you can reduce the original equation to the form

= .

dividing it by .

It gives you

= +/- + , where    is an arbitrary integer (k = 0, +/-1, +/-2, . . . ).

Hence = +/- + .

It gives for k = 0, 1, 2, 3,

= , = , , = .

Answer. = , , , .

              = , , , .

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