document.write( "Question 1009849: If 3cosx-4sinx=5,then 3sinx+4cosx=? \n" ); document.write( "

Algebra.Com's Answer #625348 by ikleyn(52855) $\"\"$ $\"About$

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\n" ); document.write( "If 3cosx - 4sinx = 5, then 3sinx + 4cosx =?
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document.write( "3*cosx - 4*sinx = 5.            (1)\r\n" );
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document.write( "Let us rewrite this equation in the form\r\n" );
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document.write( ".cos(x) - .sin(x) = 1.     (2)\r\n" );
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document.write( "Now consider the right-angled triangle with the sides (3,4,5), and let  be its smallest of two acute angles.\r\n" );
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document.write( "Then  =  and  = ,\r\n" );
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document.write( "so we can rewrite the left side of the equation (2) in the form \r\n" );
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document.write( " = 1,   or\r\n" );
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document.write( " = 1.\r\n" );
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document.write( "It implies that \r\n" );
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document.write( " =    and\r\n" );
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document.write( " = 0.                  (3)\r\n" );
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document.write( "But, from the other side, \r\n" );
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document.write( " =  + .\r\n" );
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document.write( "Now substitute here  =  and  = , and you will get\r\n" );
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document.write( " +  = .   (4)\r\n" );
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document.write( "As a last step, multiply both sides of (4) by 5, and you will get\r\n" );
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document.write( "4*cos(x) + 3*sin(x) = 0.\r\n" );
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document.write( "The problem is solved.\r\n" );
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document.write( "Answer.  If 3cosx - 4sinx = 5, then 3sinx + 4cosx = 0.\r\n" );
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