Question Number 165070 by mathlove last updated on 25/Jan/22 Answered by bobhans last updated on 25/Jan/22 $$\:\mathrm{cos}\:\mathrm{x}−\mathrm{sin}\:\mathrm{x}\:=\:\sqrt{\mathrm{1}−\mathrm{2sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}} \\ $$$$\:\Rightarrow\frac{\sqrt{\mathrm{1}−\mathrm{2sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}}}{\mathrm{sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}}\:=\:\mathrm{2}\sqrt{\mathrm{2}} \\ $$$$\sqrt{\mathrm{1}−\mathrm{2t}}\:=\:\mathrm{2}\sqrt{\mathrm{2}}\:\mathrm{t}\:,\:\left[\:\mathrm{t}=\mathrm{sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}\:\right] \\ $$$$\Rightarrow\mathrm{1}−\mathrm{2t}\:=\:\mathrm{8t}^{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{8t}^{\mathrm{2}}…
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Question Number 99433 by Dwaipayan Shikari last updated on 20/Jun/20 $${sin}\mathrm{7}\phi+{cos}\mathrm{2}\phi=−\mathrm{2} \\ $$$${Find},\phi \\ $$ Commented by bobhans last updated on 21/Jun/20 $$\mathrm{sin}\:\mathrm{7}\emptyset+\mathrm{sin}\:\left(\mathrm{90}−\mathrm{2}\emptyset\right)=−\mathrm{2} \\ $$$$\mathrm{2sin}\:\left(\frac{\mathrm{90}+\mathrm{5}\emptyset}{\mathrm{2}}\right)\:\mathrm{cos}\:\left(\frac{\mathrm{9}\emptyset−\mathrm{90}}{\mathrm{2}}\right)\:=\:−\mathrm{2}…
Question Number 99385 by Ar Brandon last updated on 20/Jun/20 $$\mathrm{Prove}\:\mathrm{sin}^{\mathrm{4}} \mathrm{A}=\frac{\mathrm{3}}{\mathrm{8}}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos2A}+\frac{\mathrm{1}}{\mathrm{8}}\mathrm{cos4A} \\ $$ Answered by Ar Brandon last updated on 20/Jun/20 $$\begin{vmatrix}{\mathrm{z}^{\mathrm{n}} −\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{n}} }=\mathrm{2}{i}\mathrm{sin}\left(\mathrm{nA}\right)\:\:,\:\:\mathrm{z}^{\mathrm{n}}…
Question Number 164912 by bobhans last updated on 23/Jan/22 $$\:\:\mathrm{If}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{9}\:,\:\mathrm{then}\:\mathrm{max}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} }{\mathrm{x}+\mathrm{y}} \\ $$ Commented by bobhans last updated on 23/Jan/22 $$\mathrm{all}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{great} \\…
Question Number 164901 by cortano1 last updated on 23/Jan/22 Answered by bobhans last updated on 23/Jan/22 $$\:\Rightarrow\:\frac{\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}}{\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}}\:−\frac{\mathrm{2}−\mathrm{3cos}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}}\:=\:\mathrm{0} \\ $$$$\Rightarrow\:\frac{\left(\mathrm{1}−\mathrm{c}\right)^{\mathrm{2}} }{\mathrm{c}^{\mathrm{2}} }\:−\frac{\mathrm{2}−\mathrm{3c}}{\mathrm{c}}\:=\:\mathrm{0}\:,\:\mathrm{c}\:=\:\mathrm{cos}\:^{\mathrm{2}}…
Question Number 99303 by Ar Brandon last updated on 20/Jun/20 Commented by Ar Brandon last updated on 20/Jun/20 I felt this could be helpful here. Especially when integrating with surds.�� Commented by MWSuSon last updated on…
Question Number 164820 by Avijit007 last updated on 22/Jan/22 Answered by Ar Brandon last updated on 22/Jan/22 $$\mathrm{Let}\:{x}\:\mathrm{and}\:{y}\:\mathrm{be}\:\mathrm{complex}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that}\:{x}={e}^{{i}\vartheta} \:\mathrm{and}\:{y}={e}^{{i}\Phi} \\ $$$$\mathrm{Then}\:{x}^{{m}} +\frac{\mathrm{1}}{{x}^{{m}} }=\mathrm{2cos}\left({m}\vartheta\right)\:\mathrm{and}\:{y}^{{m}} +\frac{\mathrm{1}}{{y}^{{m}} }=\mathrm{2cos}\left({m}\Phi\right)…
Question Number 164808 by Mathematification last updated on 22/Jan/22 Answered by mr W last updated on 22/Jan/22 Commented by mr W last updated on 22/Jan/22…