SOLUTION: Please Find the general solution of: sin3x-sinx= cos2x

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Question 1031139: Please Find the general solution of:
sin3x-sinx= cos2x

Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
Please Find the general solution of:
sin(3x) - sin(x)= cos(2x)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Apply the formula   =   to the left side.

  (Regarding this formula, see the lesson Addition and subtraction of trigonometric functions in this site).

You will get an equivalent equation

 = .

Simplify it further:

 = .

Then you have two equations:

(1)  cos(2x) = 0  --->  2x =   --->  x = , k = 0, +/-1, +/-2, . . . ,   

and

(2)  2*sin(x) = 1  --->  sin(x) =   --->  x =   and  x = , k = 0, +/-1, +/-2, . . . .

The union of the sets (1) and (2) is your solution.


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