document.write( "Question 1208813: Solve for x.\r
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Algebra.Com's Answer #847280 by ikleyn(52946) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " The solution in the post by Edwin is incomplete.\r
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document.write( "The domain (the set of real numbers, where left side of the equation\r\n" );
document.write( "is defined) is  tan(x) =/= 1.\r\n" );
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document.write( "So, the prohibited values of x are  ,  k = 0, _/-1, +/-2, . . . \r\n" );
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document.write( "We are looking for solutions of the given equation that are in its domain.\r\n" );
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document.write( "In the domain, the given equation is equivalent to\r\n" );
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document.write( "    sin(x) + cos(x) = 0,    (1)\r\n" );
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document.write( "or\r\n" );
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document.write( "    sin(x) = -cos(x).       (2)\r\n" );
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document.write( "The solutions to this equation can not be with cos(x) = 0 (since then sin(x) = 1, \r\n" );
document.write( "and this equation is not held) .\r\n" );
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document.write( "Therefore, we can divide both sides of equation (2) by cos(x).  We get then\r\n" );
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document.write( "    tan(x) = -1.\r\n" );
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document.write( "The solutions to this equation are\r\n" );
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document.write( "    x = ,  or  135° + 180°*k,  k = 0, +/-1, +/-2, . . . \r\n" );
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document.write( "ANSWER.  The solutions to the given equation are   x = ,  or  135° + 180°*k,  k = 0, +/-1, +/-2, . . . \r\n" );
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