Find all solutions to the given trigonometric equation in the interval 0, 2𝜋 : sin2x=cos2xsinx
sin^2 x - cos^ 2 xsinx = 0
sinx(sinx - cos^2 x) = 0
sinx(sinx - (1 - sin^2 x))=0
sinx = 0 or sin^2 x + sinx - 1 = 0
sinx = 0, where is the sine curve equal to zero from 0 to 2π ?
or
sinx = (-1 ± √(1-4(1)(-1)) / 2
= (-1 ± √5)/2 = .61803... or -1.618 , the latter is not admissible
x = appr .66624 or 2.4754
In total, you should have 5 solutions
(did you notice that .61803... is the decimal part of the Golden Ratio ? )