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Category: Trigonometry

Question-191102

Question Number 191102 by Mingma last updated on 18/Apr/23 Answered by mahdipoor last updated on 18/Apr/23 $${AB}={AC}={a} \\ $$$${AM}={BC}={b}=\sqrt{{a}^{\mathrm{2}} +{a}^{\mathrm{2}} −\mathrm{2}{a}^{\mathrm{2}} {cos}\mathrm{20}}=\mathrm{2}{asin}\mathrm{10} \\ $$$${BM}^{\mathrm{2}} ={AM}^{\mathrm{2}}…

nice-calculus-in-AB-C-prove-sin-2-B-sin-2-C-sin-2-A-2cos-A-sin-B-sin-C-

Question Number 125389 by mnjuly1970 last updated on 10/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:{calculus}\:… \\ $$$$\:\:\:\:\:\:\:\:{in}\:\:{A}\overset{\Delta} {{B}C}\:\:{prove}\:: \\ $$$$\:\:\:\:\:\:{sin}^{\mathrm{2}} \left({B}\right)+{sin}^{\mathrm{2}} \left({C}\right)−{sin}^{\mathrm{2}} \left({A}\right)=\mathrm{2}{cos}\left({A}\right){sin}\left({B}\right){sin}\left({C}\right) \\ $$$$ \\ $$ Answered by mnjuly1970…

Question-190875

Question Number 190875 by cortano12 last updated on 13/Apr/23 Commented by mr W last updated on 06/Aug/23 $$\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{a}}}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{b}}}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{c}}}=−\sqrt[{\mathrm{3}}]{\mathrm{10}−\sqrt[{\mathrm{3}}]{\mathrm{999}}} \\ $$$${solution}\:{see}\:{Q}#\mathrm{195628} \\ $$ Terms of Service…

Question-190874

Question Number 190874 by Rupesh123 last updated on 13/Apr/23 Answered by cortano12 last updated on 13/Apr/23 $$\left(\mathrm{1}\right)\:\mathrm{26}^{\mathrm{2}} =\left(\mathrm{a}+\mathrm{t}\right)^{\mathrm{2}} +\mathrm{t}^{\mathrm{2}} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{20}^{\mathrm{2}} =\:\left(\mathrm{a}−\mathrm{t}\right)^{\mathrm{2}} +\mathrm{t}^{\mathrm{2}} \\ $$$$\:\Rightarrow\mathrm{46}.\mathrm{6}=\left(\mathrm{2a}\right)\left(\mathrm{2t}\right)\Rightarrow\mathrm{2at}=\mathrm{46}.\mathrm{3}…

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Question Number 59683 by ranusahu last updated on 13/May/19 $${prove}\:\left(\mathrm{1}+{tanx}\right)\left(\mathrm{1}+\mathrm{tany}\right)=\mathrm{2}\:\:{if}\:\:{x}+{y}=\mathrm{45}° \\ $$$$ \\ $$ Answered by tanmay last updated on 13/May/19 $$\left(\mathrm{1}+{tanx}\right)\left(\mathrm{1}+{tan}\left(\frac{\pi}{\mathrm{4}}−{x}\right)\right) \\ $$$$\left(\mathrm{1}+{tanx}\right)\left(\mathrm{1}+\frac{\mathrm{1}−{tanx}}{\mathrm{1}+{tanx}}\right) \\…

If-2-cos-A-B-1-2sin-A-B-3-and-A-B-is-a-fine-angle-then-determine-A-s-and-B-s-value-Please-help-me-

Question Number 125073 by amns last updated on 08/Dec/20 $${If}\:\sqrt{\mathrm{2}}{cos}\left({A}\:−\:{B}\right)\:=\:\mathrm{1},\:\mathrm{2}{sin}\left({A}\:+\:{B}\right)\:=\:\sqrt{\mathrm{3}}\:{and}\:{A},\:{B}\:{is}\:{a}\:{fine} \\ $$$${angle},\:{then}\:{determine}\:{A}'{s}\:{and}\:{B}'{s}\:{value}. \\ $$$$\boldsymbol{{Please}}\:\boldsymbol{{help}}\:\boldsymbol{{me}}. \\ $$ Answered by som(math1967) last updated on 08/Dec/20 $$\mathrm{cos}\left(\mathrm{A}−\mathrm{B}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}=\mathrm{cos45} \\…