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In-ABC-then-cos-A-2-cos-B-2-cos-C-2-1-sin-A-2-1-sin-B-2-1-sin-C-2-3-3-

Question Number 170115 by Shrinava last updated on 16/May/22 $$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:\:\mathrm{then}: \\ $$$$\frac{\mathrm{cos}\:\frac{\mathrm{A}}{\mathrm{2}}\:\centerdot\:\mathrm{cos}\:\frac{\mathrm{B}}{\mathrm{2}}\:\centerdot\:\mathrm{cos}\:\frac{\mathrm{C}}{\mathrm{2}}}{\left(\mathrm{1}\:-\:\mathrm{sin}\:\frac{\mathrm{A}}{\mathrm{2}}\right)\centerdot\left(\mathrm{1}\:-\:\mathrm{sin}\:\frac{\mathrm{B}}{\mathrm{2}}\right)\centerdot\left(\mathrm{1}\:-\:\mathrm{sin}\:\frac{\mathrm{C}}{\mathrm{2}}\right)}\:\geqslant\:\mathrm{3}\sqrt{\mathrm{3}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-170100

Question Number 170100 by mathlove last updated on 16/May/22 Commented by cortano1 last updated on 16/May/22 $$\:{y}=−\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\mathrm{sin}\:{x}−\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{cos}\:{x} \\ $$$${y}=−\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:{x}+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\mathrm{sin}\:{x}\right) \\ $$$${y}=−\left(\mathrm{sin}\:\frac{\pi}{\mathrm{6}}\:\mathrm{cos}\:{x}\:+\:\mathrm{cos}\:\frac{\pi}{\mathrm{6}}\:\mathrm{sin}\:{x}\right) \\ $$$${y}=−\mathrm{sin}\:\left({x}+\frac{\pi}{\mathrm{6}}\right) \\ $$…