document.write( "Question 195575: Using tanθ = sinθ/cosθ, prove the addition formula for tangent,
\n" ); document.write( "tan(A + B) = (tan A + tan B) / (1 - tan A × tan B)\r
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Algebra.Com's Answer #148994 by arallie(162)\"\" \"About 
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tan(a + b) = [tan a + tan b]/[1 - (tan a)(tan b)]\r
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\n" ); document.write( "\n" ); document.write( "(1) tan(a + b) = sin(a + b)/cos(a + b) \r
\n" ); document.write( "\n" ); document.write( "(2) sin(a + b) = (sin a)(cos b) + (cos a)(sin b) \r
\n" ); document.write( "\n" ); document.write( "(3) cos(a + b) = (cos a)(cos b) - (sin a)(sin b) \r
\n" ); document.write( "\n" ); document.write( "(4) So that:\r
\n" ); document.write( "\n" ); document.write( "sin(a + b)/cos(a + b) = [(sin a)(cos b) + (cos a)(sin b)]/[(cos a)(cos b) - (sin a)(sin b)] =\r
\n" ); document.write( "\n" ); document.write( "(sin a)(cos b)/[(cos a)(cos b) - (sin a)(sin b)] + (cos a)(sin b)/[(cos a)(cos b) - (sin a)(sin b)]\r
\n" ); document.write( "\n" ); document.write( "(5) Multiplying both sides of the fractions by 1/(cos a)(cos b) gives us:\r
\n" ); document.write( "\n" ); document.write( "(tan a)/[1 - (tan a)(tan b)] + (tan b)/[1 - (tan a)(tan b)] =\r
\n" ); document.write( "\n" ); document.write( "= [tan a + tan b ]/[1 - (tan a)(tan b)]
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