Prove that `(sin3x+sin4X+sin5x)/(cos 2x+cos4x+cos6x)=tan4x`

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Posted on

As stated this is not an identity.

Let `x=pi/6` :

Left side `(sin((3pi)/6)+sin((4pi)/6)+sin((5pi)/6))/(cos((2pi)/6)+cos((4pi)/6)+cos((6pi)/6))`

`=(1+sqrt(3)/2+1/2)/(1/2-1/2-1)=-1/2(3+sqrt(3))~~-2.366`

Right side `tan((4pi)/6)=-sqrt(3)/2~~-1.732`

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If you meant to solve for x the solutions are `x=n(pi/4),n in ZZ`

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