document.write( "Question 1031139: Please Find the general solution of:
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Algebra.Com's Answer #645861 by ikleyn(52803)\"\" \"About 
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\n" ); document.write( "Please Find the general solution of:
\n" ); document.write( "sin(3x) - sin(x)= cos(2x)
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document.write( "Apply the formula  \"sin%28alpha%29+-+sin%28beta%29\" = \"2%2Asin%28%28alpha-beta%29%2F2%29%2Acos%28%28alpha%2Bbeta%29%2F2%29\"  to the left side.\r\n" );
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document.write( "  (Regarding this formula, see the lesson Addition and subtraction of trigonometric functions in this site).\r\n" );
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document.write( "You will get an equivalent equation\r\n" );
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document.write( "\"2%2Asin%28x%29%2Acos%282x%29\" = \"cos%282x%29\".\r\n" );
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document.write( "Simplify it further:\r\n" );
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document.write( "\"cos%282x%29%2A%282sin%28x%29-1%29\" = \"0\".\r\n" );
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document.write( "Then you have two equations:\r\n" );
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document.write( "(1)  cos(2x) = 0  --->  2x = \"2k%2Api+%2B-+pi%2F2\"  --->  x = \"k%2Api+%2B-+pi%2F4\", k = 0, +/-1, +/-2, . . . ,   \r\n" );
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document.write( "and\r\n" );
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document.write( "(2)  2*sin(x) = 1  --->  sin(x) = \"1%2F2\"  --->  x = \"pi%2F6+%2B+2k%2Api\"  and  x = \"5pi%2F6+%2B+2k%2Api\", k = 0, +/-1, +/-2, . . . .\r\n" );
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document.write( "The union of the sets (1) and (2) is your solution.\r\n" );
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