document.write( "Question 732417: 2cos^2(x/2)=(sin^2x)/(1-cosx) \n" ); document.write( "

Algebra.Com's Answer #447857 by lwsshak3(11628) $\"\"$ $\"About$

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Prove this identity:
\n" ); document.write( "2cos^2(x/2)=(sin^2x)/(1-cosx)
\n" ); document.write( "..
\n" ); document.write( "left side:
\n" ); document.write( "use cos half-angle formula:
\n" ); document.write( "2[√((1+cosx)/2)]^2=2((1+cosx)/2)=1+cosx
\n" ); document.write( "..
\n" ); document.write( "right side:(sin^2x)/(1-cosx)=(1-cos^2x)/(1-cosx)= $\"%281%2Bcosx%29cross%281-cosx%29%2Fcross%281-cosx%29\"$
\n" ); document.write( "verified:
\n" ); document.write( "left side=right side=1+cosx \n" ); document.write( "

\n" );