document.write( "Question 1015107: If x+y is less than 90 degree and sin(2x-20degree)= cos(y-10 degree) then find tan(x+y) \n" ); document.write( "
Algebra.Com's Answer #631597 by Edwin McCravy(20066)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Are you sure you didn't mean tan(2x+y)???\r\n" );
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document.write( "\"y+=+2+%28%22180%B0%22n-x%2B%2260%B0%22%29\"\r\n" );
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document.write( "Use the identity:\r\n" );
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document.write( "If sin(A) = cos(B), then A = 90°-B+360°n\r\n" );
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document.write( "sin(2x-20°)= cos(y-10°)\r\n" );
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document.write( "2x-20°= 90°-(y-10°)+360°n\r\n" );
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document.write( "2x-20°= 90°+y+10°+360°n\r\n" );
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document.write( "2x-20°= 100°+y+360°n\r\n" );
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document.write( "2x = 120°+y+360°n\r\n" );
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document.write( "2x-120°-360°n = y\r\n" );
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document.write( "x+y = x+(2x-120°-360°n)\r\n" );
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document.write( "x+y = 3x-120°-360°n \r\n" );
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document.write( "tan(x+y) = tan(3x-120°-360°n)\r\n" );
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document.write( "tan(x+y) = tan(3x-120°) = \"%28+tan%283x%29-tan%28%22120%B0%22%29+%29%2F%28+1%2Btan%283x%29tan%28%22120%B0%22%29+%29\"  \r\n" );
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document.write( " = \"%28+tan%283x%29-%28-sqrt%283%29%29+%29%2F%28+1%2Btan%283x%29%28-sqrt%283%29%29+%29\"\r\n" );
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document.write( " = \"%28+tan%283x%29%2Bsqrt%283%29+%29%2F%28+1-tan%283x%29%28sqrt%283%29%29+%29\"\r\n" );
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document.write( "tan(2x+y) works out much nicer.\r\n" );
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document.write( "Edwin
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