Question Number 143521 by SLVR last updated on 15/Jun/21 Commented by SLVR last updated on 15/Jun/21 $${kindly}\:\:{help}\:{me} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 143499 by mnjuly1970 last updated on 15/Jun/21 Commented by MJS_new last updated on 15/Jun/21 $$ \\ $$$$\mathrm{tan}\:\left(\mathrm{60}°−\alpha\right)\:=\frac{\sqrt{\mathrm{3}}−\mathrm{tan}\:\alpha}{\mathrm{1}+\sqrt{\mathrm{3}}\mathrm{tan}\:\alpha} \\ $$$$\mathrm{tan}\:\left(\mathrm{60}°+\alpha\right)\:=\frac{\sqrt{\mathrm{3}}+\mathrm{tan}\:\alpha}{\mathrm{1}−\sqrt{\mathrm{3}}\mathrm{tan}\:\alpha} \\ $$$$\mathrm{tan}\:\mathrm{3}\alpha\:=\frac{\left(\mathrm{3}−\mathrm{tan}^{\mathrm{2}} \:\alpha\right)\mathrm{tan}\:\alpha}{\mathrm{1}−\mathrm{3tan}^{\mathrm{2}} \:\alpha}…
Question Number 77959 by john santu last updated on 12/Jan/20 $${solve}\:\mathrm{tan}\:\left(\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\right)>\mathrm{1}\: \\ $$ Answered by mr W last updated on 12/Jan/20 $$\mathrm{0}<\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }<\mathrm{1} \\…
Question Number 143450 by bramlexs22 last updated on 14/Jun/21 $${when}\:{x}+{y}=\frac{\mathrm{2}\pi}{\mathrm{3}};\:{x}\geqslant\mathrm{0}\:;{y}\geqslant\mathrm{0} \\ $$$${the}\:{maximum}\:{and}\:{the}\:{minimum} \\ $$$${of}\:\mathrm{sin}\:{x}+\mathrm{sin}\:{y}\:{is}\:\_\_\_\: \\ $$ Answered by EDWIN88 last updated on 16/Jun/21 $$\:\mathrm{y}=\:\frac{\mathrm{2}\pi}{\mathrm{3}}−\mathrm{x}\:\Rightarrow\mathrm{sin}\:\mathrm{y}=\mathrm{sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{3}}−\mathrm{x}\right) \\…
Question Number 12378 by tawa last updated on 20/Apr/17 $$\mathrm{Prove}\:\mathrm{that}, \\ $$$$\mathrm{sin}\theta\:+\:\mathrm{2cos}\theta\:=\:\mathrm{1} \\ $$ Commented by mrW1 last updated on 21/Apr/17 $${this}\:{is}\:{not}\:{true}.\: \\ $$$$\theta=\mathrm{0}\Rightarrow\mathrm{sin}\:\theta+\mathrm{2cos}\:\theta=\mathrm{2}\neq\mathrm{1} \\…
Question Number 143439 by ERA last updated on 14/Jun/21 $$\mathrm{sinx}+\mathrm{sin2x}+\mathrm{sin3x}+…..+\mathrm{sinkx}=\mathrm{sin}\frac{\mathrm{kx}}{\mathrm{2}}×\frac{\mathrm{sin}\frac{\mathrm{k}+\mathrm{1}}{\mathrm{2}}\mathrm{x}}{\mathrm{sin}\frac{\mathrm{x}}{\mathrm{2}}} \\ $$$$\mathrm{prove} \\ $$ Answered by Mathspace last updated on 14/Jun/21 $${A}_{{n}} ={sinx}+{sin}\left(\mathrm{2}{x}\right)+…+{sin}\left({nx}\right)\:\Rightarrow \\ $$$${A}_{{n}}…
Question Number 143350 by gsk2684 last updated on 13/Jun/21 $$\mathrm{if}\:\mathrm{tan}^{\mathrm{2}} \alpha\mathrm{tan}^{\mathrm{2}} \beta+\mathrm{tan}^{\mathrm{2}} \beta\mathrm{tan}^{\mathrm{2}} \gamma+ \\ $$$$\mathrm{tan}^{\mathrm{2}} \gamma\mathrm{tan}^{\mathrm{2}} \alpha+\mathrm{2tan}^{\mathrm{2}} \alpha\mathrm{tan}^{\mathrm{2}} \beta\mathrm{tan}^{\mathrm{2}} \gamma=\mathrm{1} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{sin}^{\mathrm{2}} \alpha+\mathrm{sin}^{\mathrm{2}} \beta+\mathrm{sin}^{\mathrm{2}}…
Question Number 143348 by gsk2684 last updated on 13/Jun/21 $$\mathrm{if}\:\:\frac{\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}}{\mathrm{cos}\:^{\mathrm{2}} \mathrm{y}}+\frac{\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{y}}=\mathrm{1}\:\mathrm{then}\: \\ $$$$\mathrm{find}\:\frac{\mathrm{cos}\:^{\mathrm{4}} \mathrm{y}}{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}}+\frac{\mathrm{sin}\:^{\mathrm{4}} \mathrm{y}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}=? \\ $$ Answered by som(math1967)…
Question Number 143274 by Aditya9886 last updated on 12/Jun/21 Answered by Olaf_Thorendsen last updated on 12/Jun/21 $${y}\:=\:\mathrm{sin}^{\mathrm{2}} \left(\mathrm{cos}{x}\right) \\ $$$$\frac{{dy}}{{dx}}\:=\:\left(−\mathrm{sin}{x}\right)×\mathrm{2cos}\left(\mathrm{cos}{x}\right)×\mathrm{sin}\left(\mathrm{cos}{x}\right) \\ $$$$\frac{{dy}}{{dx}}\:=\:−\mathrm{sin}{x}.\mathrm{sin}\left(\mathrm{2cos}{x}\right) \\ $$$$ \\…
Question Number 12132 by tawa last updated on 14/Apr/17 $$\mathrm{Given}\:\mathrm{that}\:\:\mathrm{1}°\:=\:\mathrm{0}.\mathrm{017}\:\mathrm{rad} \\ $$$$\mathrm{Use}\:\:\mathrm{f}\left(\mathrm{a}\right)\:=\:\mathrm{sin}\left(\mathrm{a}\right)\:\mathrm{to}\:\mathrm{find}\:\mathrm{an}\:\mathrm{approximate}\:\mathrm{value}\:\mathrm{for}\:\mathrm{sin}\left(\mathrm{29}\right)°. \\ $$ Answered by mrW1 last updated on 14/Apr/17 $$\frac{\Delta{y}}{\Delta{x}}=\frac{{f}\left({x}+\Delta{x}\right)−{f}\left({x}\right)}{\Delta{x}}\approx\frac{{dy}}{{dx}} \\ $$$$\Rightarrow\:{f}\left({x}+\Delta{x}\right)\approx{f}\left({x}\right)+\frac{{dy}}{{dx}}\Delta{x} \\…