Mark M. answered 02/25/16
Tutor
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Retired Math prof with teaching and tutoring experience in trig.
The equation is clearly not an identity. For example, try it when x = 0.
The equation is true sometimes. To solve the equation for x, we can proceed as follows:
cos(2x) = 1 - 2sin2x
So, the given equation is equivalent to the equation:
1 - 2sin2x - 3sinx = 2
2sin2x + 3sinx + 1 = 0
(2sinx + 1)(sinx + 1) = 0
sinx = -1/2 or sinx = -1
x = 7π/6. 11π/6, 3π/2 (solutions between 0 and 2π)
Add any multiple of 2π to these 3 answers to find other solutions.