document.write( "Question 420224: verify each of the following identities
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\n" ); document.write( "\n" ); document.write( "prob. 1. sin(A-B)/sinAsinB = cotB-cotA \r
\n" ); document.write( "\n" ); document.write( "prob. 2. tan A/2 + cot A/2 = 2cscA \n" ); document.write( "
Algebra.Com's Answer #293949 by lwsshak3(11628)\"\" \"About 
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prob. 1. sin(A-B)/sinAsinB = cotB-cotA
\n" ); document.write( "prob. 2. tan A/2 + cot A/2 = 2cscA\r
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\n" ); document.write( "\n" ); document.write( "1. sin(A-B)/sinAsinB = cotB-cotA
\n" ); document.write( "Starting with left side,
\n" ); document.write( "sinACosB-cosAsinB/sinAsinB
\n" ); document.write( "Divide both terms by sinAsinB
\n" ); document.write( "sinACosB/sinAsinB-cosAsinB/sinAsinB
\n" ); document.write( "cosB/sinB-cosA/sinA=cotB-cotA
\n" ); document.write( "verified: Left-hand side=right-hand side\r
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\n" ); document.write( "2. tan A/2 + cot A/2 = 2cscA
\n" ); document.write( "starting with left side
\n" ); document.write( "tan(1/2)A=sinA/1+cosA
\n" ); document.write( "cot(1/2)A=reciprocal of tan (1/2)A=1+cosA/sinA
\n" ); document.write( "=sinA/1+cosA+1+cosA/sinA
\n" ); document.write( "LCD=(sinA)(1+cosA)
\n" ); document.write( "=sin^2A+1+2cosA+cos^2A/(sinA)(1+cosA)
\n" ); document.write( "=2+2cosA/(sinA)(1+cosA)
\n" ); document.write( "=2(1+cosA)/(sinA)(1+cosA)
\n" ); document.write( "=2/sinA=2cscA
\n" ); document.write( "verified:Left-hand side=right-hand side \r
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