SOLUTION: If sinA+cosA=7/5 and sinA cosA=12/25, find sinA-cosA

Question 515298: If sinA+cosA=7/5 and sinA cosA=12/25, find sinA-cosA
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
If sinA+cosA=7/5 and sinA cosA=12/25, find sinA-cosA
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sinA cosA=12/25
2sinA cosA = 24/25
sin(2A) = 24/25
A = (arcsin(24/25))/2
sin(A) = 0.6
cos(A) = 0.8
sin - cos = +/-0.2
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Or
cosA = 7/5 - sin(A)
sin*(7/5 - sin) = 12/25
sin^2 - (7/5)sin + 12/25 = 0
Sub x for sin
25x^2 - 35x + 12 = 0
(5x - 3)*(5x - 4) = 0
x = 3/5, 4/5
sin = 3/5, cos = 4/5 or vice versa
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