document.write( "Question 1207278: cos(2x+10)=sin(x+20)
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Algebra.Com's Answer #845060 by ikleyn(52943) $\"\"$ $\"About$

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document.write( "The given equation is  cos(2x+10) = sin(x+20).\r\n" );
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document.write( "It is assumed that the arguments of sine and cosine are in degrees.\r\n" );
document.write( "Also, it is assumed, that the solution should be found in the interval 0 <= x < 360 degrees.\r\n" );
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document.write( "Use the identity cos(90-theta) = sin(theta)\r\n" );
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document.write( "Substituting the values we get,\r\n" );
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document.write( "    90-theta = 2x+10      (1)\r\n" );
document.write( "       theta = x+20       (2)\r\n" );
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document.write( "We have simultaneous equations in two unknowns.\r\n" );
document.write( "Exclude theta by adding equations 1 and 2\r\n" );
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document.write( "    90-theta+theta = 2x+10+x+20\r\n" );
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document.write( "    90 = 3x+30\r\n" );
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document.write( "    3x+30 = 90\r\n" );
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document.write( "    3x = 90-30 = 60\r\n" );
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document.write( "    x = 20\r\n" );
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document.write( "ANSWER.  x = 20 degrees.\r\n" );
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