SOLUTION: Solve for the exact solutions arcsin(x)+arctan(x)=0 Help!!!

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Question 743897: Solve for the exact solutions

arcsin(x)+arctan(x)=0
Help!!!
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
arcsin%28x%29%2Barctan%28x%29=0

arctan%28x%29=-arcsin%28x%29

arcsine is an odd function so we "pull" the negative sign into the input...

arctan%28x%29=arcsin%28-x%29

tan%28arctan%28x%29%29=tan%28arcsin%28-x%29%29

The tangent of arcsine is...
x%2Fsqrt%281-x%5E2%29


so we simplify...
x=%28-x%29%2Fsqrt%281-x%5E2%29
x%2Asqrt%281-x%5E2%29=-x
x%2Asqrt%281-x%5E2%29%2Bx=0
x%2A%28sqrt%281-x%5E2%29%2B1%29=0
By the zero product rule
x=0
or
sqrt%281-x%5E2%29%2B1=0
But the equation can never have a real solution (why?)

...so x=0