SOLUTION: find all the solutions in the interval 0-x-2pi of the equation 2cos(squared)x+1 = 5sinx giving each solution in terms of pi

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Question 857742: find all the solutions in the interval 0-x-2pi of the equation
2cos(squared)x+1 = 5sinx
giving each solution in terms of pi
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
2%2A%28cos%28x%29%29%5E2%2B1+=+5%2Asin%28x%29
Substitute,
%28cos%28x%29%29%5E2=1-%28sin%28x%29%29%5E2
.
.
2%2A%281-%28sin%28x%29%29%5E2%29%2B1+=+5%2Asin%28x%29
2-2%28sin%28x%29%29%5E2%2B1=5sin%28x%29
2%28sin%28x%29%29%5E2%2B5sin%28x%29-3=0
Substitute u=sin%28x%29
2u%5E2%2B5u-3=0
%282u-1%29%28u%2B3%29=0
Two "u" solutions:
2u-1=0
2u=1
u=1%2F2
sin%28x%29=1%2F2
x=%281%2F6%29pi and x=%285%2F6%29pi
and
u%2B3=0
u=-3
sin%28x%29=-3
No x solution from this u solution since abs%28sin%28x%29%29%3C=1