SOLUTION: Use trigonometric identities to solve sin^2(theta) - cos^2(theta) = sin(theta) exactly for 0 < theta

SOLUTION: Use trigonometric identities to solve sin^2(theta) - cos^2(theta) = sin(theta) exactly for 0 < theta < 2\pi

Question 680161: Use trigonometric identities to solve sin^2(theta) - cos^2(theta) = sin(theta) exactly for 0 < theta < 2\pi
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Use trigonometric identities to solve sin^2(theta) - cos^2(theta) = sin(theta) exactly for 0 < theta < 2pi
**
sin^2x-cos^2x=sinx
sin^2x-(1-sin^2x)-sinx=0
sin^2x-1+sin^2x-sinx=0
2sin^2x-sinx-1=0
(2sinx+1)(sinx-1)=0
2sinx+1=0
sinx=-1/2
x=7π/6, 11π/6 (in QIII and QIV where sin<0)
or
sinx-1=0
sinx=1
x=π/2

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