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Question Number 115253 by aye48 last updated on 24/Sep/20

Express sin 4x interm of sin x.

$$\mathrm{Express}\:\mathrm{sin}\:\mathrm{4x}\:\mathrm{interm}\:\mathrm{of}\:\mathrm{sin}\:\mathrm{x}. \\ $$

Answered by Dwaipayan Shikari last updated on 24/Sep/20

sin4x=2sin2xcos2x  =2sinxcosx(1−2sin^2 x)  =2sinx(√(1−sin^2 x)) (1−2sin^2 x)

$$\mathrm{sin4x}=\mathrm{2sin2xcos2x} \\ $$$$=\mathrm{2sinxcosx}\left(\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} \mathrm{x}\right) \\ $$$$=\mathrm{2sinx}\sqrt{\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\:\left(\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} \mathrm{x}\right) \\ $$

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