SOLUTION: Write the trig function as an algebraic expression: sin(2arctanx) PLEASE HELP ME!!! I really don't know what to do.

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Question 180507: Write the trig function as an algebraic expression: sin(2arctanx)
PLEASE HELP ME!!! I really don't know what to do.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You have to say this one in a way that makes sense
In words:
First, "arctan(x)" means "the angle whose tangent is x"
Therefore, "2*arctan(x)" means twice the angle whose tangent is x"
Now I can read the whole thing as:
"the sine of twice the angle whose tangent is x"
If the tangent is x%2F1, then the sine is x%2Fsqrt%28x%5E2+%2B+1%29
and the cosine is 1%2Fsqrt%28x%5E2+%2B+1%29
The double angle formula for sine is:
sin%282a%29+=+2%2Asin%28a%29%2Acos%28a%29
sin%282a%29+=+2%2A%28x%2Fsqrt%28x%5E2+%2B+1%29%29%2A%281%2Fsqrt%28x%5E2+%2B+1%29%29
sin%282a%29+=+%282x%29+%2F+%28x%5E2+%2B+1%29 answer
Suppose the angle was 45 degrees. Then x=1 and
sin%282a%29+=+%282x%29+%2F+%28x%5E2+%2B+1%29
sin%2890%29+=+2+%2F+2
sin%2890%29+=+1 and this is true