document.write( "Question 1152875: let x and y are acute angles, tan(x). tan(y) =1,
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Algebra.Com's Answer #775030 by ikleyn(52914) $\"\"$ $\"About$

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document.write( "Let x be the greater of the two given acute angles, and let y be the smaller.\r\n" );
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document.write( "Then, first, the equality  tan(x)*tan(y) = 1  implies that\r\n" );
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document.write( "    x + y = 90°.         (1)\r\n" );
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document.write( "Second, \r\n" );
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document.write( "    tan(x-y) =  = \r\n" );
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document.write( "         substitute given values for the numerator and denominator to get\r\n" );
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document.write( "              =  =  = ,\r\n" );
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document.write( "which implies  \r\n" );
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document.write( "    x - y = 60°.           (2)\r\n" );
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document.write( "From equations (1) and (2), by adding, you get\r\n" );
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document.write( "    2x = 90° + 60° = 150°;   hence,  x =  = 75°.\r\n" );
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document.write( "Finally, substituting this value of x into (1), you get  y = 15°.\r\n" );
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document.write( "So, under the given conditions,  x = 75°  and  y = 15°.\r\n" );
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document.write( "In particular,  x = 5y.\r\n" );
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