document.write( "Question 971377: Find all solutions of each equation on the interval(0, 2pi)
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Algebra.Com's Answer #854517 by ikleyn(53853) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "        The solution in the post by @lwsshak3 is incorrect (incomplete).\r
\n" ); document.write( "\n" ); document.write( "        He provided only one root of the equation in his answer, and gave incorrect value for it.\r
\n" ); document.write( "\n" ); document.write( "        while the problem has two roots. So, one root was determined incorrectly, while the second root was missed. \r
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\n" ); document.write( "\n" ); document.write( "        I came to bring a correct solution.\r
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document.write( "sec^2 x + 2tan x = 0\r\n" );
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document.write( "lcd: cos^2(x)\r\n" );
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document.write( "1 + 2sin(x)*cos(x) = 0\r\n" );
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document.write( "1 + sin(2x) = 0\r\n" );
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document.write( "sin(2x) = -1\r\n" );
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document.write( "2x = , k = 0, +/-1, +/-2, . . . \r\n" );
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document.write( "We take only two values  2x =   (k=0)  and  2x =   (k=1),\r\n" );
document.write( "since other values produce values of x out of the given interval.\r\n" );
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document.write( "ANSWER.  The given equation has two roots in the interval  [,).\r\n" );
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document.write( "         They are , or 135 degrees,  and  , or 315 degrees.\r\n" );
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