Question 870626: Find all real numbers in the interval [0, 2pi) that satisfy each equation.
1. 3sinx+3=2cos^2x
2. sinx^2x=cos^2x
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find all real numbers in the interval [0, 2pi) that satisfy each equation.
1. 3sinx+3=2cos^2x
3sinx+3=2(1-sin^2x)
sinx+3=2-2sin^2x
2sin^2x+sinx+1=0
(2sinx+1)(sinx+1)=0
..
2sinx+1=0
sinx=-1/2
x=3π/6, 11π/6
or
sinx+1=0
sinx=-1
x=3π/2
..
2. sinx^2x=cos^2x
sin^2x-cos^2x=0
cos(2x)=0
2x=π/2, 3π/2
x=π/4, 3π/4
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