document.write( "Question 664860: How do I answer step by step the identity 1/2 cot x/2 - 1/2 tan x/2 = cot x. I have spent several hours working on this problem and I can't figure it out. \n" ); document.write( "
Algebra.Com's Answer #413486 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
How do I answer step by step the identity 1/2 cot x/2 - 1/2 tan x/2 = cot x.
\n" ); document.write( "**
\n" ); document.write( "Identity:tan (x/2)=(sin x)/(1+cos x)
\n" ); document.write( "cot (x/2)=1/tan (x/2)=(1+cos x)/(sin x)
\n" ); document.write( "..
\n" ); document.write( "1/2 cot x/2 - 1/2 tan x/2 = cot x
\n" ); document.write( "start with left side:
\n" ); document.write( "1/2 cot x/2 - 1/2 tan x/2
\n" ); document.write( "=(1+cos x)/2(sin x)-(sin x)/2(1+cos x)
\n" ); document.write( "LCD: 2sin x(1+cos x)
\n" ); document.write( "=(1+cos x)^2-sin^2x)/(2sin x(1+cos x)
\n" ); document.write( "=(1+2cos x+cos^2x-sin^2x)/(2sin x(1+cos x)
\n" ); document.write( "1-sin^2x=cos^2x
\n" ); document.write( "=(2cos x+2cos^2x)/(2sin x(1+cos x)
\n" ); document.write( "=(cos x+cos^2x)/(sin x(1+cos x)
\n" ); document.write( "=(cos x(1+cos x)/(sin x(1+cos x)
\n" ); document.write( "=cos x/sin x
\n" ); document.write( "=cot x
\n" ); document.write( "verified: left side=right side\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );