Question Number 143641 by mathlove last updated on 16/Jun/21 $$\mathrm{sin}\:\mathrm{160}−\mathrm{sin}\:\mathrm{20}=? \\ $$ Answered by Rasheed.Sindhi last updated on 16/Jun/21 $$\mathrm{sin}\:\mathrm{160}−\mathrm{sin}\:\mathrm{20} \\ $$$$=\mathrm{sin}\left(\mathrm{180}−\mathrm{20}\right)−\mathrm{sin}\:\mathrm{20} \\ $$$$=\mathrm{sin180cos20}−\mathrm{cos180sin20}−\mathrm{sin20} \\…
Question Number 12572 by tawa last updated on 25/Apr/17 $$\mathrm{prove}\:\mathrm{that}\:\mathrm{if}, \\ $$$$\mathrm{sin}\left(\theta\right)\:=\:\frac{\mathrm{1}\:−\:\mathrm{x}}{\mathrm{1}\:+\:\mathrm{x}}\:\:\:\:\:\mathrm{then}\:\:\mathrm{tan}\left(\frac{\mathrm{x}}{\mathrm{4}}\:−\:\frac{\theta}{\mathrm{2}}\right)\:=\:\sqrt{\mathrm{x}} \\ $$ Commented by mrW1 last updated on 26/Apr/17 $${I}\:{think}\:{you}\:{mean}\:\mathrm{t}{a}\mathrm{n}\left(\frac{\pi}{\mathrm{4}}\:−\:\frac{\theta}{\mathrm{2}}\right)\:=\:\sqrt{\mathrm{x}} \\ $$ Answered…
Question Number 12532 by tawa last updated on 24/Apr/17 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\::\:\:\mathrm{p} \\ $$$$\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{2x}\right)\:+\:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{3x}\right)\:=\:\frac{\pi}{\mathrm{4}} \\ $$ Answered by mrW1 last updated on 25/Apr/17 $$\mathrm{tan}\:\left[\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{2x}\right)\:+\:\mathrm{tan}^{−\mathrm{1}}…
Question Number 12525 by tawa last updated on 24/Apr/17 $$\mathrm{Use}\:\mathrm{the}\:\mathrm{substitution}\:\:\mathrm{t}\:=\:\mathrm{sin}\left(\theta\right)\:\mathrm{to}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\mathrm{2sin}^{\mathrm{4}} \left(\theta\right)\:−\:\mathrm{9sin}^{\mathrm{3}} \left(\theta\right)\:+\:\mathrm{14sin}^{\mathrm{2}} \left(\theta\right)\:−\:\mathrm{9sin}\left(\theta\right)\:+\:\mathrm{2}\:=\:\mathrm{0},\:\: \\ $$$$\mathrm{for}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\theta\:\mathrm{in}\:\mathrm{the}\:\mathrm{range}\:\:\mathrm{0}\:\leqslant\:\theta\:\leqslant\:\mathrm{2}\pi \\ $$ Answered by mrW1 last updated on…
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}}…