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Category: Trigonometry

Show-that-Area-blue-circle-Area-Green-circle-

Question Number 198828 by a.lgnaoui last updated on 24/Oct/23 $$\:\:\boldsymbol{\mathrm{Show}}\:\boldsymbol{\mathrm{th}{at}}: \\ $$$$\:\boldsymbol{{Area}}\left(\boldsymbol{{blue}}\:\boldsymbol{{circle}}\right)=\boldsymbol{{Area}}\left(\boldsymbol{{Green}}\:\:\boldsymbol{{circle}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$ Commented by a.lgnaoui last updated on 24/Oct/23 Answered by…

let-a-R-z-C-resolve-z-1-n-e-ipina-deduce-that-P-n-k-0-n-1-sin-a-kpi-n-

Question Number 198357 by pticantor last updated on 18/Oct/23 $$\boldsymbol{{let}}\:\:\boldsymbol{{a}}\in\mathbb{R},\:\boldsymbol{{z}}\in\mathbb{C} \\ $$$$\boldsymbol{{resolve}}\: \\ $$$$\left(\boldsymbol{{z}}+\mathrm{1}\right)^{\boldsymbol{{n}}} =\boldsymbol{{e}}^{\boldsymbol{{i}}\pi\boldsymbol{{na}}} \\ $$$$\boldsymbol{{deduce}}\:\boldsymbol{{that}}\:\boldsymbol{{P}}_{\boldsymbol{{n}}} =\underset{{k}=\mathrm{0}} {\overset{\boldsymbol{{n}}−\mathrm{1}} {\prod}}\boldsymbol{{sin}}\left(\boldsymbol{{a}}+\frac{\boldsymbol{{k}}\pi}{\boldsymbol{{n}}}\right) \\ $$ Terms of Service…

3-sin-2-tan-cos-2-

Question Number 197937 by mathlove last updated on 05/Oct/23 $$\sqrt{\mathrm{3}}\:{sin}^{\mathrm{2}} \theta\centerdot{tan}\beta+{cos}^{\mathrm{2}} \beta=? \\ $$ Answered by Frix last updated on 05/Oct/23 $$\mathrm{It}\:\mathrm{is}\:\mathrm{what}\:\mathrm{it}\:\mathrm{is},\:\mathrm{not}\:\mathrm{getting}\:\mathrm{better}\:\mathrm{any}\:\mathrm{way}. \\ $$$${p}=\mathrm{tan}\:\theta\:\wedge{q}=\mathrm{tan}\:\beta\:\rightarrow\:\frac{\sqrt{\mathrm{3}}{p}^{\mathrm{2}} {q}}{{p}^{\mathrm{2}}…