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Category: Trigonometry

when-x-y-2pi-3-x-0-y-0-the-maximum-and-the-minimum-of-sin-x-sin-y-is-

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) \\…

Prove-that-sin-2cos-1-

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} \\…

sinx-sin2x-sin3x-sinkx-sin-kx-2-sin-k-1-2-x-sin-x-2-prove-

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}}…

if-tan-2-tan-2-tan-2-tan-2-tan-2-tan-2-2tan-2-tan-2-tan-2-1-then-find-sin-2-sin-2-sin-2-

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}}…

if-cos-4-x-cos-2-y-sin-4-x-sin-2-y-1-then-find-cos-4-y-cos-2-x-sin-4-y-sin-2-x-

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-143274

Question Number 143274 by Aditya9886 last updated on 12/Jun/21 Answered by Olaf_Thorendsen last updated on 12/Jun/21 $${y}\:=\:\mathrm{sin}^{\mathrm{2}} \left(\mathrm{cos}{x}\right) \\ $$$$\frac{{dy}}{{dx}}\:=\:\left(−\mathrm{sin}{x}\right)×\mathrm{2cos}\left(\mathrm{cos}{x}\right)×\mathrm{sin}\left(\mathrm{cos}{x}\right) \\ $$$$\frac{{dy}}{{dx}}\:=\:−\mathrm{sin}{x}.\mathrm{sin}\left(\mathrm{2cos}{x}\right) \\ $$$$ \\…

Given-that-1-0-017-rad-Use-f-a-sin-a-to-find-an-approximate-value-for-sin-29-

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} \\…

Question-12085

Question Number 12085 by chux last updated on 12/Apr/17 Answered by ajfour last updated on 12/Apr/17 $${let}\:\mathrm{6}°=\theta \\ $$$$\mathrm{sin}\:\mathrm{24}°=\mathrm{2sin}\:\mathrm{12}°\mathrm{cos}\:\mathrm{12}° \\ $$$${let}\:\mathrm{sin}\:\mathrm{12}°={x}\:\:{and}\:\:\mathrm{cos}\:\mathrm{12}°={y} \\ $$$$\mathrm{sin}\:\left(\mathrm{3}\theta+\mathrm{2}\theta\right)=\:{y}\:\mathrm{sin}\:\mathrm{18}°+{x}\:\mathrm{cos}\:\mathrm{18}° \\ $$$$\Rightarrow\:{x}\mathrm{cos}\:\mathrm{18}°+{y}\mathrm{sin}\:\mathrm{18}°\:=\mathrm{sin}\:\mathrm{5}\theta=\frac{\mathrm{1}}{\mathrm{2}}…

If-tan-2-1-2tan-2-then-prove-that-cos-2-1-2cos-2-

Question Number 12078 by agni5 last updated on 12/Apr/17 $$\mathrm{If}\:\mathrm{tan}\:^{\mathrm{2}} \alpha\:=\:\mathrm{1}+\mathrm{2tan}\:^{\mathrm{2}} \beta\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\:\mathrm{cos}\:\mathrm{2}\beta\:=\mathrm{1}+\mathrm{2cos}\:\mathrm{2}\alpha\:. \\ $$ Answered by ajfour last updated on 12/Apr/17 $$\mathrm{1}+\mathrm{2cos}\:\mathrm{2}\alpha\:=\mathrm{1}+\frac{\mathrm{2}\left(\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \alpha\right)}{\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}}…