document.write( "Question 180507: Write the trig function as an algebraic expression: sin(2arctanx)
\n" ); document.write( "PLEASE HELP ME!!! I really don't know what to do. \n" ); document.write( "

Algebra.Com's Answer #135306 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
You have to say this one in a way that makes sense
\n" ); document.write( "In words:
\n" ); document.write( "First, \"arctan(x)\" means \"the angle whose tangent is x\"
\n" ); document.write( "Therefore, \"2*arctan(x)\" means twice the angle whose tangent is x\"
\n" ); document.write( "Now I can read the whole thing as:
\n" ); document.write( "\"the sine of twice the angle whose tangent is x\"
\n" ); document.write( "If the tangent is $\"x%2F1\"$ , then the sine is $\"x%2Fsqrt%28x%5E2+%2B+1%29\"$
\n" ); document.write( "and the cosine is $\"1%2Fsqrt%28x%5E2+%2B+1%29\"$
\n" ); document.write( "The double angle formula for sine is:
\n" ); document.write( " $\"sin%282a%29+=+2%2Asin%28a%29%2Acos%28a%29\"$
\n" ); document.write( " $\"sin%282a%29+=+2%2A%28x%2Fsqrt%28x%5E2+%2B+1%29%29%2A%281%2Fsqrt%28x%5E2+%2B+1%29%29\"$
\n" ); document.write( " $\"sin%282a%29+=+%282x%29+%2F+%28x%5E2+%2B+1%29\"$ answer
\n" ); document.write( "Suppose the angle was 45 degrees. Then $\"x=1\"$ and
\n" ); document.write( " $\"sin%282a%29+=+%282x%29+%2F+%28x%5E2+%2B+1%29\"$
\n" ); document.write( " $\"sin%2890%29+=+2+%2F+2\"$
\n" ); document.write( " $\"sin%2890%29+=+1\"$ and this is true
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