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Category: Trigonometry

Question-219839

Question Number 219839 by Lekhraj last updated on 02/May/25 Answered by golsendro last updated on 03/May/25 $$\:\mathrm{sin}\:\mathrm{2}\theta\:=\:\mathrm{2}\left(\frac{\sqrt{\mathrm{4}−\sqrt{\mathrm{5}}}\:+\sqrt{\sqrt{\mathrm{5}}−\mathrm{2}}}{\mathrm{2}}\:\right)\left(\frac{\sqrt{\mathrm{4}−\sqrt{\mathrm{5}}}−\sqrt{\sqrt{\mathrm{5}}−\mathrm{2}}}{\mathrm{2}}\:\right) \\ $$$$\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{4}−\sqrt{\mathrm{5}}\:−\sqrt{\mathrm{5}}\:+\mathrm{2}\:\right) \\ $$$$\:=\:\mathrm{3}−\sqrt{\mathrm{5}}\: \\ $$ Terms of…

Question-219279

Question Number 219279 by Mingma last updated on 22/Apr/25 Answered by som(math1967) last updated on 22/Apr/25 $$\:\frac{\mathrm{2}{sin}\frac{\beta+\alpha}{\mathrm{2}}{cos}\frac{\alpha−\beta}{\mathrm{2}}}{\mathrm{2sin}\:\frac{\alpha+\beta}{\mathrm{2}}{sin}\frac{\alpha−\beta}{\mathrm{2}}}=\sqrt{\mathrm{3}} \\ $$$$\Rightarrow\:{cot}\frac{\alpha−\beta}{\mathrm{2}}={cot}\frac{\pi}{\mathrm{6}} \\ $$$$\Rightarrow\:\:\alpha−\beta=\frac{\pi}{\mathrm{3}} \\ $$$$\:\mathrm{sin}\:\mathrm{3}\alpha+\mathrm{sin}\:\beta \\ $$$$=\mathrm{2sin}\:\frac{\mathrm{3}\left(\alpha+\beta\right)}{\mathrm{2}}×\mathrm{cos}\:\frac{\mathrm{3}\left(\alpha−\beta\right)}{\mathrm{2}}…

Prove-that-sin351-4-10-2-5-8-

Question Number 217384 by MATHEMATICSAM last updated on 12/Mar/25 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{sin351}°\:=\:−\:\sqrt{\frac{\mathrm{4}\:−\:\sqrt{\mathrm{10}\:+\:\mathrm{2}\sqrt{\mathrm{5}}}}{\mathrm{8}}\:.} \\ $$ Answered by Sutrisno last updated on 14/Mar/25 $${cos}\mathrm{18}°=\frac{\sqrt{\mathrm{10}+\mathrm{2}\sqrt{\mathrm{5}}}}{\mathrm{4}} \\ $$$${sin}\mathrm{351}°=−{sin}\mathrm{9}° \\ $$$$=−\sqrt{\frac{\mathrm{1}−{cos}\mathrm{18}°}{\mathrm{2}}} \\…

determiner-le-cote-du-care-ABCD-inscrit-dans-l-elipse-3-3-8-8-

Question Number 217146 by a.lgnaoui last updated on 02/Mar/25 $$\mathrm{determiner}\:\mathrm{le}\:\mathrm{cote}\:\mathrm{du}\:\mathrm{care}\:\boldsymbol{\mathrm{ABCD}} \\ $$$$\mathrm{inscrit}\:\mathrm{dans}\:\mathrm{l}\:\mathrm{elipse}\:\left\{\left(−\mathrm{3},+\mathrm{3}\right):\left(−\mathrm{8},+\mathrm{8}\right)\right\} \\ $$ Commented by a.lgnaoui last updated on 02/Mar/25 Answered by mr W…

Comparto-otro-reto-de-matematicas-que-dice-literalmente-Hallar-las-ecuaciones-de-3-circunferencias-mutuamente-tangentes-y-de-radios-los-3-iguales-Este-reto-depende-en-que-cuadrante-se-repre

Question Number 216733 by josemanuelrios last updated on 17/Feb/25 $$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Comparto}\:\mathrm{otro}\:\mathrm{reto}\:\mathrm{de}\:\mathrm{matematicas}\:\mathrm{que}\: \\ $$$$\mathrm{dice}\:\mathrm{literalmente}: \\…