SOLUTION: Solve for x arccos(2-3x) = 2arcsin(x)

Algebra ->  Trigonometry-basics -> SOLUTION: Solve for x arccos(2-3x) = 2arcsin(x)       Log On


   

Question 1161852: Solve for x
arccos(2-3x) = 2arcsin(x)



Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
arccos(2-3x) = 2arcsin(x)

Take the cosine of both sides:

cos%28arccos%282-3x%29%5E%22%22%29=+cos%282arcsin%28x%29%5E%22%22%29

The left side is just 2-3x.  For the right side let:
                              
                                   arcsin(x) = θ
                                      sin(θ) = x 
                                     
2-3x=cos%282theta%29
2-3x=1-2sin%5E2%28theta%29
2-3x=1-2x%5E2%29
2x%5E2-3x%2B1=0
%282x-1%29%28x-1%29=0

Two solutions: 1/2 and 1

Edwin