SOLUTION: Solve for x: 4sin^2x+sinx+3=6cos^2x

Question 1081158: Solve for x: 4sin^2x+sinx+3=6cos^2x
Answer by ikleyn(52910) (Show Source): You can put this solution on YOUR website!
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4sin^2x+sinx+3=6cos^2x
~~~~~~~~~~~~~~~~~~~~~~~~

 =   ---> (replace cos^2(x) by 1-sin^2(x))  --->

 = ,

 = ,

 = 0.

Introduce new variable y = sin(x). Then the last equation takes the form

 = 0.

Its roots, according to the quadratic formula, are

 =  = .


1.   =  =   --->  sin(x) =   --->  x =   and/or  x = .


2.   =  =   --->  sin(x) =   --->  x =   and/or  x = .


Answer.  The original equation has 4 solutions:  , ,  and .

Plot y = (red) and y = (green)

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