document.write( "Question 1153180: If arctan(x)=arccos(y), show that
\n" ); document.write( " $\"y+=1%2Fsqrt%281%2Bx%5E2%29\"$ . \n" ); document.write( "

Algebra.Com's Answer #775355 by Edwin McCravy(20065) $\"\"$ $\"About$

You can put this solution on YOUR website!
If arctan(x)=arccos(y), show that
\n" ); document.write( " $\"y+=1%2Fsqrt%281%2Bx%5E2%29\"$
\n" ); document.write( "

\r\n" );
document.write( "Let the angle that both sides equal be θ: \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and since \r\n" );
document.write( "\r\n" );
document.write( ",\r\n" );
document.write( "\r\n" );
document.write( "we can draw two similar right triangles with angle θ, one\r\n" );
document.write( "for each side of the equation.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We use the Pythagorean theorem to find the missing sides:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Because they are similar right triangles,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );