document.write( "Question 1113956: If sinx+cosx=-1/5, and $\"+3pi%2F4+\"$ ≤x≤pi, find the value of cos2x. \n" ); document.write( "

Algebra.Com's Answer #729024 by ikleyn(52812) $\"\"$ $\"About$

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document.write( "If  sinx + cosx = -1/5,   then, squaring both sides\r\n" );
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document.write( " = ,   or,  replacing   by 1\r\n" );
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document.write( "1 + 2*sin(x)*cos(x) = ,  and hense\r\n" );
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document.write( "2*sin(x)*cos(x) =  = .\r\n" );
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document.write( "Since  2*sin(x)*cos(x) = sin(2x),  you get\r\n" );
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document.write( "sin(2x) = .\r\n" );
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document.write( "Next, since   <= x <= , you have  for 2x    <= 2x <= ,  i.e.  2x lies in QIV.\r\n" );
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document.write( "Therefore,  cos(2x) =  =  =  =  =  = .\r\n" );
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document.write( "The sign at sqrt is \"+\" (plus)  since cosine is positive in QIV.\r\n" );
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document.write( "Answer.  cos(2x) = .\r\n" );
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