SOLUTION: solve each equation 23) 3 - sin theta = cos(2 theta)

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Question 712342: solve each equation

23) 3 - sin theta = cos(2 theta)
Answer by lwsshak3(11628) About Me  (Show Source):
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3 - sin theta = cos(2 theta)
3-sinx=cos2x
3-sinx=1-2sin^2x
sin^2x-sinx+2=0
(sinx-1)(sinx+2)=0
sinx+2=0
sinx=-2 (reject, (-1 ≤ x ≤ 1))
sinx-1=0
sinx=1
x=π/2