document.write( "Question 1040337: For what value of x does the eq 4sinx+3sin2x-2sin3x+sin4x =2root3
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Algebra.Com's Answer #655157 by ikleyn(52797) $\"\"$ $\"About$

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document.write( "I can not solve this equation in the strong sense: I can not find all the roots.\r\n" );
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document.write( "But I can guess one root: x =  = 30 deg.\r\n" );
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document.write( "Indeed, then\r\n" );
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document.write( "sin(x)  =  ;         4sin(x)  =   = 2;\r\n" );
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document.write( "sin(2x) = ;         3sin(2x) = ;\r\n" );
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document.write( "sin(3x) = {{1}}};      2sin(3x) = ;\r\n" );
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document.write( "sin(4x) = ;          sin(4x) = .\r\n" );
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document.write( "Therefore,  4sin(x) + 3sin(2x) - 2sin(3x) + sin(4x) = 2 +  - 2 +  =  = .    QED.\r\n" );
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document.write( "The problem does not require to find all solution.\r\n" );
document.write( "It asks to find at least one solution.\r\n" );
document.write( "One solution is found.\r\n" );
document.write( "Thus the problem is solved.\r\n" );
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