To find sin(x) * cos(x), we need to first solve the equation sin(x) + cos(x) = 1/3.
Given sin(x) + cos(x) = 1/3, we can square both sides of the equation to get rid of the square root:
(sin(x) + cos(x))^2 = (1/3)^2sin^2(x) + 2sin(x)cos(x) + cos^2(x) = 1/9
Now, we know that sin^2(x) + cos^2(x) = 1, so we can substitute this in:
1 + 2sin(x)cos(x) = 1/92sin(x)cos(x) = 1/9 - 12sin(x)cos(x) = -8/9
Divide by 2 to solve for sin(x) * cos(x):
sin(x)cos(x) = -8/18sin(x)cos(x) = -4/9
Therefore, sin(x) * cos(x) = -4/9.
To find sin(x) * cos(x), we need to first solve the equation sin(x) + cos(x) = 1/3.
Given sin(x) + cos(x) = 1/3, we can square both sides of the equation to get rid of the square root:
(sin(x) + cos(x))^2 = (1/3)^2
sin^2(x) + 2sin(x)cos(x) + cos^2(x) = 1/9
Now, we know that sin^2(x) + cos^2(x) = 1, so we can substitute this in:
1 + 2sin(x)cos(x) = 1/9
2sin(x)cos(x) = 1/9 - 1
2sin(x)cos(x) = -8/9
Divide by 2 to solve for sin(x) * cos(x):
sin(x)cos(x) = -8/18
sin(x)cos(x) = -4/9
Therefore, sin(x) * cos(x) = -4/9.