SOLUTION: For what value of x does the eq 4sinx+3sin2x-2sin3x+sin4x =2root3

Question 1040337: For what value of x does the eq 4sinx+3sin2x-2sin3x+sin4x =2root3

Answer by ikleyn(52792) (Show Source): You can put this solution on YOUR website!
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For what value of x does the equation 4sinx+3sin2x-2sin3x+sin4x = 2root3
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I can not solve this equation in the strong sense: I can not find all the roots.

But I can guess one root: x =  = 30 deg.


Indeed, then

sin(x)  =  ;         4sin(x)  =   = 2;

sin(2x) = ;         3sin(2x) = ;

sin(3x) = {{1}}};      2sin(3x) = ;

sin(4x) = ;          sin(4x) = .

Therefore,  4sin(x) + 3sin(2x) - 2sin(3x) + sin(4x) = 2 +  - 2 +  =  = .    QED.

The problem does not require to find all solution.
It asks to find at least one solution.
One solution is found.
Thus the problem is solved.

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