document.write( "Question 1208912: Solve for x.\r
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Algebra.Com's Answer #847432 by ikleyn(52817) $\"\"$ $\"About$

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\n" ); document.write( "2sinx + 2tanx = 0
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document.write( "You want to solve\r\n" );
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document.write( "    2sin(x) + 2tan(x) = 0.\r\n" );
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document.write( "The domain of this equation are all real numbers except of  x = ,  where cos(x) = 0.\r\n" );
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document.write( "Rewrite in the form\r\n" );
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document.write( "    2sin(x) +  = 0.\r\n" );
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document.write( "In the domain, multiply both sides by  .\r\n" );
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document.write( "Since  cos(x) =/= 0,  you will get an equivalent equation\r\n" );
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document.write( "    sin(x)*cos(x) + sin(x) = 0.\r\n" );
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document.write( "Factor\r\n" );
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document.write( "    sin(x)*(cos(x) + 1) = 0.\r\n" );
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document.write( "So, either sin(x) = 0,  giving the solutions  x = ,  k = 0, +/-1, +/-2, . . .          (1)\r\n" );
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document.write( "    or  cos(x) + 1 = 0,  cos(x) = -1,  giving  x = ,  k = 0, +/-1, +/-2, . . .    (2)\r\n" );
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document.write( "The set (2) is part of set (1) - so, the general solution to the given equation is the set\r\n" );
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document.write( "    x = ,  k = 0, +/-1, +/-2, . . .\r\n" );
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document.write( "ANSWER.  The general solution to the given equation is the set  x = ,  k = 0, +/-1, +/-2, . . .\r\n" );
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