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Category: Trigonometry

Question-211496

Question Number 211496 by RojaTaniya last updated on 11/Sep/24 Answered by som(math1967) last updated on 11/Sep/24 $$\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{2}{sin}\mathrm{20}{sin}\mathrm{40}+\mathrm{2}{sin}\mathrm{20}{sin}\mathrm{60}+\mathrm{2}{sin}\mathrm{20}{sin}\mathrm{80}\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\left({cos}\mathrm{20}−{cos}\mathrm{60}+{cos}\mathrm{40}−{cos}\mathrm{80}+{cos}\mathrm{60}−{cos}\mathrm{100}\right) \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\left({cos}\mathrm{20}+{cos}\mathrm{40}−{cos}\mathrm{80}+{cos}\mathrm{80}\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{2}{cos}\mathrm{30}{cos}\mathrm{10} \\ $$$$={sin}\mathrm{60}{sin}\mathrm{80}…

ABC-cos-C-sin-A-cos-A-2-sin-B-cos-B-2-Find-cos-C-

Question Number 211392 by CrispyXYZ last updated on 08/Sep/24 $$\bigtriangleup{ABC}.\:\mathrm{cos}\:{C}=\frac{\mathrm{sin}\:{A}\:+\:\mathrm{cos}\:{A}}{\mathrm{2}}=\frac{\mathrm{sin}\:{B}\:+\:\mathrm{cos}\:{B}}{\mathrm{2}}. \\ $$$$\mathrm{Find}\:\mathrm{cos}\:{C}. \\ $$ Answered by Frix last updated on 08/Sep/24 $$\mathrm{Rectangular}\:\mathrm{triangle} \\ $$$$\mathrm{cos}\:{A}\:=\mathrm{sin}\:{B}\:\wedge\:\mathrm{sin}\:{A}\:=\:\mathrm{cos}\:{B}\:\Rightarrow\:{C}=\mathrm{90}° \\…

Prove-in-AB-C-cosA-sin-2-A-cosB-sin-2-B-cosC-sin-2-C-r-R-r-incircle-radius-R-circumcircle-radius-

Question Number 211276 by mnjuly1970 last updated on 04/Sep/24 $$ \\ $$$$\:\:{Prove}\:,\:{in}\:{A}\overset{\Delta} {{B}C}\:\::\: \\ $$$$ \\ $$$$\:\:\:\:\:\frac{{cosA}}{{sin}^{\mathrm{2}} {A}}\:+\:\frac{{cosB}}{{sin}^{\mathrm{2}} {B}}\:\:+\frac{{cosC}}{{sin}^{\mathrm{2}} {C}}\:\geqslant\:\frac{{r}}{{R}} \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:{r}\::\:{incircle}\:\:{radius} \\…

Question-211115

Question Number 211115 by Durganand last updated on 28/Aug/24 Answered by som(math1967) last updated on 28/Aug/24 $${tanA}+\mathrm{2}{tan}\mathrm{2}{A}+\frac{\mathrm{4}}{{tan}\mathrm{2}.\mathrm{2}{A}} \\ $$$$={tanA}+\mathrm{2}{tan}\mathrm{2}{A}+\frac{\mathrm{4}\left(\mathrm{1}−{tan}^{\mathrm{2}} \mathrm{2}{A}\right)}{\mathrm{2}{tan}\mathrm{2}{A}} \\ $$$$={tanA}+\frac{\mathrm{2}{tan}^{\mathrm{2}} \mathrm{2}{A}+\mathrm{2}−\mathrm{2}{tan}^{\mathrm{2}} \mathrm{2}{A}}{{tan}\mathrm{2}{A}}\: \\…

Question-210677

Question Number 210677 by Safojon last updated on 16/Aug/24 Answered by BHOOPENDRA last updated on 16/Aug/24 $$\theta=\frac{{k}\pi}{\mathrm{7}\:},\mathrm{7}\theta={k}\pi\:\left({where}\:{k}=\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}….{n}\right) \\ $$$$\mathrm{7}\theta=\pi\:\left({k}=\mathrm{1}\right) \\ $$$$\mathrm{4}\theta+\mathrm{3}\theta=\pi \\ $$$${tg}\mathrm{4}\theta=−{tg}\left(\mathrm{3}\theta\right)\:{let}\:{tg}={t} \\ $$$$\Rightarrow\:\frac{\mathrm{4}{t}−\mathrm{4}{t}^{\mathrm{3}}…