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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}° \\…

Question-211393

Question Number 211393 by BaliramKumar last updated on 08/Sep/24 Commented by BaliramKumar last updated on 08/Sep/24 $${a}^{\mathrm{2}} −{b}^{\mathrm{2}} \:=\:\mathrm{25}\:\:\:\:\:\:\:\:\:\:\:{a}+{b}\:=\:\mathrm{5} \\ $$$$\left({a}−{b}\right)\left({a}+{b}\right)\:=\:\mathrm{25} \\ $$$$\left({a}−{b}\right)\mathrm{5}\:=\:\mathrm{25} \\ $$$${a}−{b}\:=\:\mathrm{5}………\left({i}\right)…

soit-le-systeme-d-equatiins-x-y-z-7-x-2-y-2-z-2-9-xyz-5-1-x-1-y-1-z-

Question Number 211368 by a.lgnaoui last updated on 07/Sep/24 $$\mathrm{soit}\:\mathrm{le}\:\mathrm{systeme}\:\mathrm{d}\:\mathrm{equatiins} \\ $$$$\:\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{z}}\:\:\:\:=\mathrm{7} \\ $$$$\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} +\boldsymbol{\mathrm{z}}^{\mathrm{2}} =\mathrm{9} \\ $$$$\:\:\boldsymbol{\mathrm{xyz}}\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{5} \\ $$$$ \\ $$$$\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{z}}}? \\ $$…

F-0-0-F-1-1-F-n-1-F-n-F-n-1-prove-1-89-i-1-10-i-F-i-1-

Question Number 211370 by liuxinnan last updated on 07/Sep/24 $${F}\left(\mathrm{0}\right)=\mathrm{0}\:\:\:\:\:\:\:{F}\left(\mathrm{1}\right)=\mathrm{1}\:\:\:\:{F}\left({n}+\mathrm{1}\right)={F}\left({n}\right)+{F}\left({n}−\mathrm{1}\right) \\ $$$${prove}: \\ $$$$\frac{\mathrm{1}}{\mathrm{89}}=\underset{{i}=\mathrm{1}} {\overset{+\infty} {\sum}}\mathrm{10}^{−{i}} {F}\left({i}−\mathrm{1}\right) \\ $$ Answered by mr W last updated…

Question-211381

Question Number 211381 by Spillover last updated on 07/Sep/24 Commented by MathematicalUser2357 last updated on 10/Sep/24 $$\mathrm{Is}\:\mathrm{it}\:\int_{\mathrm{0}} ^{\mathrm{ln}\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)} \mathrm{sinh}^{\mathrm{3}} {x}\:\mathrm{cosh}^{\mathrm{11}} {x}\:{dx} \\ $$ Answered by…