The general solution of $$sin$$ x $$-$$ $$3sin$$ $$2x$$ $$+$$ $$sin$$ $$3x$$ $$=$$ $$cos$$ x $$-3cos$$ $$2x$$ $$+$$ $$cos$$ $$3x$$ is

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Infinity Learn · Accepted Answer

∵$$sin$$⁡x−$$3sin$$⁡$$2x+$$$$sin$$⁡$$3x=$$$$cos$$⁡x−$$3cos$$⁡$$2x+$$$$cos$$⁡$$3x($$$$sin$$⁡$$3x+$$$$sin$$⁡$$x)$$−$$3sin$$⁡$$2x=($$$$cos$$⁡$$3x+$$$$cos$$⁡$$x)$$−$$3cos$$⁡$$2x2sin$$⁡$$2x$$⋅$$cos$$⁡x−$$3sin$$⁡$$2x=2cos$$⁡$$2x$$⋅$$cos$$⁡x−$$3cos$$⁡$$2xsin$$⁡$$2x(2cos$$⁡x−$$3)$$−$$cos$$⁡$$2x(2cos$$⁡x−$$3)=0($$$$sin$$⁡$$2x$$−$$cos$$⁡$$2x)(2cos$$⁡x−$$3)=0So$$, $$sin$$⁡$$2x$$−$$cos$$⁡$$2x=0as$$  $$2cos$$⁡x−$$3$$≠$$0now$$, $$sin$$⁡$$2x=$$$$cos$$⁡$$2xtan$$⁡$$2x=1=$$$$tan$$⁡π$$42x=n$$π$$+$$π$$4x=n$$$$π$$$$2+$$π$$8$$

The general solution of sin x - 3sin 2x + sin 3x = cos x -3cos 2x + cos 3x is

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