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Question Number 75504 by mathocean1 last updated on 12/Dec/19

$$\mathrm{please}\mathrm{sirs}\mathrm{i}\mathrm{would}\mathrm{like}\mathrm{that}\mathrm{you}\mathrm{help}\mathrm{me}\mathrm{to}$$$$\mathrm{show}\mathrm{this}:$$$$\sin (\frac{\pi }{3}+\mathrm{x})\sin (\frac{\pi }{3}-\mathrm{x})=\frac{3}{4}-{\sin }^2\mathrm{x}$$

Answered by som(math1967) last updated on 12/Dec/19

$$sin(\frac{\pi }{3}+x)sin(\frac{\pi }{3}-x)$$$$={sin}^2\frac{\pi }{3}-{sin}^{2}x★$$$$=\frac{3}{4}-{sin}^{2}x$$$$★sin(A+B)sin(A-B)={sin}^{2}A-{sin}^{2}B$$

Commented by mathocean1 last updated on 12/Dec/19

$$\mathrm{thank}\mathrm{you}\mathrm{sir}$$

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