document.write( "Question 1207278: cos(2x+10)=sin(x+20)
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Algebra.Com's Answer #845074 by Edwin McCravy(20066)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Ikleyn gave only one solution, but there are 4 solutions for \"0%3C=x%3C360\"\r\n" );
document.write( "and infinitely many by adding 360on to each of the four.\r\n" );
document.write( "Every number is considered in degrees.\r\n" );
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document.write( "cos(2x+10)=sin(x+20)\r\n" );
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document.write( "This is a case of cos(A)=sin(B)\r\n" );
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document.write( "\"cos%28A%29=sin%28B%29=cos%2890-B%29=cos%28B-90%29=cos%2890-B%2B360n%29=cos%28B-90%2B360n%29\"\r\n" );
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document.write( "For the case \r\n" );
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document.write( "\"cos%28A%29=cos%2890-B%2B360n%29\"\r\n" );
document.write( "\"A+=+90-B%2B360n\"\r\n" );
document.write( "\"2x%2B10=90-%28x%2B20%29%2B360n\"\r\n" );
document.write( "which simplifies to\r\n" );
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document.write( "\"x=20%2B120n\"\r\n" );
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document.write( "This gives us the solutions 20o, 140o, 260o,\r\n" );
document.write( "between 0o and 360o.\r\n" );
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document.write( "However, this may not be all possible solutions \"0%5Eo%3C=x%3C=360%5Eo\"\r\n" );
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document.write( "We must also consider the case\r\n" );
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document.write( "\"cos%28A%29=cos%28B-90%2B360n%29\"\r\n" );
document.write( "\"A=B-90%2B360n\"\r\n" );
document.write( "\"2x%2B10=%28x%2B20%29-90%2B360n\"\r\n" );
document.write( "which simplifies to\r\n" );
document.write( "\"x=360n-80\"\r\n" );
document.write( "This gives us only one additional solution 280o between 0o and 360o.\r\n" );
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document.write( "So all the solutions in \"0%3C=x%3C360\" are\r\n" );
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document.write( "20o, 140o, 260o, and 280o.\r\n" );
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document.write( "To get all infinitely many solutions, add 360no to all four. \r\n" );
document.write( "(n is any integer, positive, negative or 0.)\r\n" );
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document.write( "Edwin
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