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Please Find the general solution of:
sin(3x) - sin(x)= cos(2x)
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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.