document.write( "Question 1128743: Given cos (theta/2) = a and sin (2 theta) = b, find tan (theta)
\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #745240 by ikleyn(52803)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "1.  If   \"cos%28theta%2F2%29\" = a,  then  \"cos%28theta%29\" = \"2%2Acos%5E2%28theta%2F2%29-1\" = \"2%2Aa%5E2-1\".        (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2.  If  \"sin%282%2Atheta%29\" = b,  then  \"2%2Asin%28theta%29%2Acos%28theta%29\" = b,\r\n" );
document.write( "\r\n" );
document.write( "    hence,  \"sin%28theta%29\" = \"b%2F%282%2Acos%28theta%29%29\" = (substitute from (1)) = \"b%2F%282%2A%282%2Aa%5E2-1%29%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "3.  Then  \"tan%28theta%29\" = \"sin%28theta%29%2Fcos%28theta%29\" = \"b%2F%282%2A%282%2Aa%5E2-1%29%29\" : \"%282a%5E2-1%29%29\" = \"b%2F%282%2A%282a%5E2-1%29%5E2%29\".        ANSWER \r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );