document.write( "Question 1153160: If sin(x)+cos(x) = -1/5, and 3pi/4 ≤ x ≤ pi, find the value of cos(2x) \n" ); document.write( "

Algebra.Com's Answer #775349 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "It can be done in much simpler manner.\r\n" );
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document.write( "Start from the given equation\r\n" );
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document.write( "    sin(x) + cos(x) = .\r\n" );
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document.write( "Square both sides\r\n" );
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document.write( "    sin^2(x) + 2*sin(x)*cos(x) + cos^2(x) = .\r\n" );
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document.write( "Replace  sin^x) + cos^2(x) by 1\r\n" );
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document.write( "    1 + 2*sin(x)*cos(x) = \r\n" );
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document.write( "Replace 2*sin(x)*cos(x) by sin(2x)\r\n" );
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document.write( "    sin(2x) =  - 1,   or   sin(2x) = .\r\n" );
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document.write( "Hence, cos^2(2x) =  =  =  =  = .\r\n" );
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document.write( "Since the angle (2x) is in QIV, cos(2x) is positive.\r\n" );
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document.write( "Hence,  cos(2x) = positive square root of  =  = .\r\n" );
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document.write( "The proof is completed.\r\n" );
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