The answer depends on x,
on whether x is measured in degrees or radians
and on whether the question is about sin(x) - 2 or sin(x - 2).
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[sin(x)^3 + cos(x)^3] / [sin(x) + cos(x)]= [(sin(x) + cos(x))(sin(x)^2 - sin(x)cos(x) + cos(x)^2)] / [sin(x) + cos(x)]***Now you can cancel a "sin(x) + cos(x)" from the top and bottom of the fraction. This makes the bottom of the fraction equal to 1. I am just going to write the next step without a 1 on the bottom of the fraction (x/1=x).So now you just have:= (sin(x)^2 - sin(x)cos(x) + cos(x)^2) *I'm going to move some terms around now. ~Not doing any computation in this step.= (sin(x)^2 + cos(x)^2 - sin(x)cos(x)) *Now we know that cos(x)^2 + sin(x)^2 = 1.= 1 - sin(x)cos(x)
2 sin(x) - 3 = 0 2 sin(x) = 3 sin(x) = 1.5 No solution. The maximum value of the sine function is 1.0 .
d/dx [sin(x) + 2] = cos(x)
-3
10x^2 - x - 2 = (5x + 2)(2x - 1)