Question Number 128130 by physicstutes last updated on 04/Jan/21 $$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\:\mathrm{sin}\left(\mathrm{2}{x}\:+\:\mathrm{2}{h}\right)−\mathrm{sin}\:\mathrm{2}{x}\:=\:\mathrm{2cos}\left(\mathrm{2}{x}\:+{h}\right)\mathrm{sin}\:{h} \\ $$ Answered by Olaf last updated on 04/Jan/21 $$\mathrm{sin}{a}−\mathrm{sin}{b}\:=\:\mathrm{2sin}\left(\frac{{a}−{b}}{\mathrm{2}}\right)\mathrm{cos}\left(\frac{{a}+{b}}{\mathrm{2}}\right)\:\left(\mathrm{1}\right) \\ $$$${a}\:=\:\mathrm{2}{x}+\mathrm{2}{h}\:\mathrm{and}\:{b}\:=\:\mathrm{2}{x} \\…
Question Number 128094 by TITA last updated on 04/Jan/21 $$\mathrm{solve}\:\mathrm{for}\:\mathrm{x}\:\:\mathrm{in}\:\:\:\mathrm{0}\leqslant\mathrm{x}\leqslant\mathrm{2}\pi \\ $$$$\mathrm{sin}\:\mathrm{2x}=\mathrm{sec}\:\mathrm{x} \\ $$ Answered by MJS_new last updated on 04/Jan/21 $$\mathrm{sin}\:\mathrm{2}{x}\:=\mathrm{2sin}\:{x}\:\mathrm{cos}\:{x} \\ $$$$\mathrm{sin}\:{x}\:={s} \\…
Question Number 128068 by benjo_mathlover last updated on 04/Jan/21 $$\:\mathrm{Given}\:\mathrm{25x}^{\mathrm{2}} −\mathrm{30x}+\mathrm{7}=\mathrm{0}\:\mathrm{has}\:\mathrm{the} \\ $$$$\mathrm{roots}\:\mathrm{are}\:\mathrm{cos}\:\alpha\:\mathrm{and}\:\mathrm{cos}\:\beta.\:\mathrm{If}\:\mathrm{cos}\:\alpha−\mathrm{cos}\:\beta>\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\:\left(\frac{\alpha+\beta}{\mathrm{2}}\right).\mathrm{tan}\:\left(\frac{\alpha−\beta}{\mathrm{2}}\right)\:=? \\ $$ Answered by bemath last updated on 04/Jan/21 $$\:\mathrm{let}\:\frac{\alpha+\beta}{\mathrm{2}}=\mathrm{x}\:\wedge\:\frac{\alpha−\beta}{\mathrm{2}}=\mathrm{y}…
Question Number 128010 by Study last updated on 03/Jan/21 Commented by Study last updated on 03/Jan/21 $${help}\:{me}\:{and}\:{show}\:{practice} \\ $$ Commented by som(math1967) last updated on…
Question Number 62431 by rajesh4661kumar@gamil.com last updated on 21/Jun/19 Answered by tanmay last updated on 21/Jun/19 $${asin}^{\mathrm{2}} \theta+{bcos}^{\mathrm{2}} \theta={c} \\ $$$${asin}^{\mathrm{2}} \theta+{b}\left(\mathrm{1}−{sin}^{\mathrm{2}} \theta\right)={c} \\ $$$${sin}^{\mathrm{2}}…
Question Number 127944 by liberty last updated on 03/Jan/21 $$\:\mathrm{If}\:\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{then}\:\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}\:+\:\mathrm{cos}\:^{\mathrm{3}} \mathrm{x}\:=? \\ $$ Answered by mr W last updated on 03/Jan/21 $${p}_{{n}} =\mathrm{sin}^{{n}} \:{x}+\mathrm{cos}^{{n}}…
Question Number 62347 by rajesh4661kumar@gamil.com last updated on 20/Jun/19 Answered by Kunal12588 last updated on 20/Jun/19 $$\frac{{csc}\:\theta\:−\:{sin}\:\theta}{{sec}\:\theta\:−\:{cos}\:\theta}\:=\:\frac{{a}^{\mathrm{3}} }{{b}^{\mathrm{3}} } \\ $$$$\Rightarrow{cot}\:\theta\:\frac{\mathrm{1}−{sin}^{\mathrm{2}} \theta}{\mathrm{1}−{cos}^{\mathrm{2}} \theta}=\frac{{a}^{\mathrm{3}} }{{b}^{\mathrm{3}} }…
Question Number 127877 by rs4089 last updated on 02/Jan/21 Commented by rs4089 last updated on 02/Jan/21 $${prove}\:{it}… \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 127835 by bemath last updated on 02/Jan/21 $$\:\mathrm{If}\:\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{10}} {\prod}}\:\mathrm{cos}\:\left(\frac{\mathrm{k}\pi}{\mathrm{11}}\right)\:=\:−\mathrm{2}^{\mathrm{n}} \:,\:\mathrm{then}\:\mathrm{n}\:=\:? \\ $$$$ \\ $$ Answered by liberty last updated on 02/Jan/21 $$\:\mathrm{let}\:\mathrm{Y}\:=\:\mathrm{cos}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{2x}\:\mathrm{cos}\:\mathrm{3x}\:\mathrm{cos}\:\mathrm{4x}\:…
Question Number 127814 by dactor last updated on 02/Jan/21 Answered by mnjuly1970 last updated on 02/Jan/21 $${solution} \\ $$$$\mathrm{2}{cos}^{\mathrm{2}} \left({x}\right)−\mathrm{1}−{cos}\left({x}\right)+\mathrm{1}=\mathrm{0} \\ $$$$\Rightarrow{cos}\left({x}\right)\left(\mathrm{2}{cos}\left({x}\right)−\mathrm{1}\right)=\mathrm{0} \\ $$$${cos}\left({x}\right)=\mathrm{0}\Rightarrow\:{x}=\mathrm{2}{k}\pi\:\:;\:{k}\in\mathbb{Z} \\…