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proof-that-sin-1sin-2-sin-n-sin-pi-n-sin-2pi-n-sin-n-1-pi-n-for-n-N-0-1-

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Question Number 178 by 123456 last updated on 14/Dec/14
proof that ∣sin 1sin 2...sin n∣≤sin (π/n)sin ((2π)/n)...sin (((n−1)π)/n) for ∀n∈N\{0,1}
$$\mathrm{proof}\:\mathrm{that} \\ $$$$\mid\mathrm{sin}\:\mathrm{1sin}\:\mathrm{2}…\mathrm{sin}\:{n}\mid\leqslant\mathrm{sin}\:\frac{\pi}{{n}}\mathrm{sin}\:\frac{\mathrm{2}\pi}{{n}}…\mathrm{sin}\:\frac{\left({n}−\mathrm{1}\right)\pi}{{n}} \\ $$$$\mathrm{for}\:\forall{n}\in\mathbb{N}\backslash\left\{\mathrm{0},\mathrm{1}\right\} \\ $$

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