document.write( "Question 378302: Hey, I'm trying to prove this sin(u+v)=sin(u)cos(v)+cos(u)sin(v) and I have no idea how. Thanks :) \n" ); document.write( "

Algebra.Com's Answer #268807 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "By the law of sines,\r\n" );
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document.write( "Let those three fractions equal to a constant k,\r\n" );
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document.write( "Then we have\r\n" );
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document.write( "VW = k*sin(U), UW = k*sin(V), UV = k*sin(W)\r\n" );
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document.write( "Draw altitude WX\r\n" );
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document.write( "VX = VW*cos(V) = k*sin(U)cos(V) \r\n" );
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document.write( "UX = UW*cos(U) = k*sin(V)cos(U)\r\n" );
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document.write( "UV = VX + UX = k*sin(U)cos(V) + k*sin(V)cos(U)\r\n" );
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document.write( "UV = k*sin(W)\r\n" );
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document.write( "k*sin(W) = k*sin(U)cos(V) + k*sin(V)cos(U)\r\n" );
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document.write( "sin(W) = sin(U)cos(V) + sin(V)cos(U)\r\n" );
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document.write( "W = 180° - (U+V)\r\n" );
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document.write( "sin[180°-(U+V)] = sin(U)cos(V) + sin(V)cos(U)\r\n" );
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document.write( "and since the sine of the supplement of an angle \r\n" );
document.write( "equals the sine of the angle,\r\n" );
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document.write( "sin(U+V) = sin(U)cos(V) + sin(V)cos(U)\r\n" );
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document.write( "switch the factors in the last term\r\n" );
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document.write( "sin(U+V) = sin(U)cos(V) + cos(U)sin(V)\r\n" );
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document.write( "Edwin

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