document.write( "Question 680161: Use trigonometric identities to solve sin^2(theta) - cos^2(theta) = sin(theta) exactly for 0 < theta < 2\pi \n" ); document.write( "
Algebra.Com's Answer #422274 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
Use trigonometric identities to solve sin^2(theta) - cos^2(theta) = sin(theta) exactly for 0 < theta < 2pi
\n" ); document.write( "**
\n" ); document.write( "sin^2x-cos^2x=sinx
\n" ); document.write( "sin^2x-(1-sin^2x)-sinx=0
\n" ); document.write( "sin^2x-1+sin^2x-sinx=0
\n" ); document.write( "2sin^2x-sinx-1=0
\n" ); document.write( "(2sinx+1)(sinx-1)=0
\n" ); document.write( "2sinx+1=0
\n" ); document.write( "sinx=-1/2
\n" ); document.write( "x=7π/6, 11π/6 (in QIII and QIV where sin<0)
\n" ); document.write( "or
\n" ); document.write( "sinx-1=0
\n" ); document.write( "sinx=1
\n" ); document.write( "x=π/2\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );