Algebra.Com's Answer #653598 by ikleyn(52832)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Find all solutions of the equation in the interval [0, 2pi).\r
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document.write( "Sec^2x - secx = 2
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document.write( " =  .\r\n" );
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document.write( "Introduce new variable u = seq(x). Then your equation becomes\r\n" );
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document.write( " = ,\r\n" );
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document.write( " =  .\r\n" );
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document.write( "Factor the left side. You will get\r\n" );
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document.write( "(u-2)*(u+1) = 0.\r\n" );
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document.write( "The solutions are \r\n" );
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document.write( "u = 2 and/or u = -1.\r\n" );
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document.write( "From this point you have two equations:\r\n" );
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document.write( "1) sec(x) = 2 --->  = 2 ---> cos(x) =  ---> x = +/- +  , k = 0, +/-1, +/-2, . . . and\r\n" );
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document.write( "2) sec(x) = -1 ---> = -1 ---> cos(x) =  ---> x =  + , k = 0, +/-1, +/-2, . . .\r\n" );
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document.write( "Answer. x = +/- + , k = 0, +/-1, +/-2, . . . and\r\n" );
document.write( " x =  , k = 0, +/-1, +/-2, . . .\r\n" );
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document.write( "Solved.\r
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