document.write( "Question 963442: prove that 2 cos square theta+3 sin theta=0 \n" ); document.write( "

Algebra.Com's Answer #588619 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
You can't prove it because it's not an identity.
\n" ); document.write( "You need to solve the equation for the values of theta for which this equation holds.
\n" ); document.write( " $\"2cos%5E2%28theta%29%2B3sin%28theta%29=0\"$
\n" ); document.write( " $\"2%281-sin%5E2%28theta%29%29%2B3sin%28theta%29=0\"$
\n" ); document.write( " $\"-2sin%5E2%28theta%29%2B3sin%28theta%29%2B2=0\"$
\n" ); document.write( " $\"2sin%5E2%28theta%29-3sin%28theta%29-2=0\"$
\n" ); document.write( "Substitute, $\"u=sin%28theta%29\"$
\n" ); document.write( " $\"2u%5E2-3u-2=0\"$
\n" ); document.write( " $\"%28u-2%29%282u%2B1%29=0\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"u-2=0\"$
\n" ); document.write( " $\"u=2\"$
\n" ); document.write( " $\"sin%28theta%29=2\"$
\n" ); document.write( "No solution exists.
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"2u%2B1=0\"$
\n" ); document.write( " $\"2u=-1\"$
\n" ); document.write( " $\"u=-1%2F2\"$
\n" ); document.write( " $\"sin%28theta%29=-1%2F2\"$
\n" ); document.write( " $\"theta=210\"$ and $\"theta=330\"$
\n" ); document.write( " \n" ); document.write( "

\n" );