Algebra.Com's Answer #729008 by ikleyn(52794)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Angles A and B are acute angles such that tanA+tanB+(tanA)(tanB)=1. If A-B=41°, find the measure of angle A.
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document.write( "It is nice non-standard Trigonometry problem.
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document.write( "I will show you how to solve it.\r
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document.write( "You are given\r\n" );
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document.write( "tan(A) + tan(B) + (tan(A))*(tan(B)) = 1.\r\n" );
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document.write( "It implies\r\n" );
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document.write( "tan(A) + tan(B) = 1 - (tan(A))*(tan(B)), and, after dividing both sides by the right side\r\n" );
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document.write( " = 1.\r\n" );
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document.write( "The left side is nothing else as tan(A+B), according to the adding formula for tangent function. So your equation takes the form\r\n" );
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document.write( "tan(A+B) = 1,\r\n" );
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document.write( "and, since the angles A and B are acute, it implies that\r\n" );
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document.write( "A + B = 45 degrees.\r\n" );
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document.write( "So, now you have two equations:\r\n" );
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document.write( "A + B = 45 (1)\r\n" );
document.write( "A - B = 41 (2)\r\n" );
document.write( "------------------------- Add the equations to eliminate B. You will get\r\n" );
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document.write( "2A = 45 + 41 = 86 ====> A =  = 43.\r\n" );
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document.write( "Thus the angle A = 43°.\r\n" );
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document.write( "Then from equation (1), B = 45° - 43° = 2°.\r\n" );
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document.write( "Answer. Angle A = 43°. Angle B = 2°.\r\n" );
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document.write( "Solved.\r
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