SOLUTION: Please help me solve these 3 equations for solutions from [0, 2pi]: 1.) {{{2cos^2(2x)-cos2x=0}}} 2.) {{{2sin^2(x)-sin(x)-1=0}}} 3.) {{{tan^2(3x)=-tan(3x)}}} Thank you!!

Question 983506: Please help me solve these 3 equations for solutions from [0, 2pi]:
1.)
2.)
3.)
Thank you!!!
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!

1. - = .

Introduce new variable    = .

Then your equation will be

- = .

One solution is = , i.e.    = , which gives    = or    = .
Please complete this case yourself.

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

- = ,   i.e.    = .

It gives you    = , and then    = or    = = .

You can complete this case yourself.

The remaining equations can be solved using the same trick with introduction of a new variable.

You can do it yourself.

Good luck !!!

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