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Author: Tinku Tara

prove-that-sin-3x-2cos-3x-2-sin-3x-2-

Question Number 129233 by MrJoe last updated on 14/Jan/21 $${prove}\:{that} \\ $$$${sin}\:\mathrm{3}{x}=\mathrm{2}{cos}\left(\frac{\mathrm{3}{x}}{\mathrm{2}}\right){sin}\left(\frac{\mathrm{3}{x}}{\mathrm{2}}\right) \\ $$ Commented by MrJoe last updated on 15/Jan/21 $${then}\: \\ $$$${if}\:{sin}\left(\mathrm{3}{x}\right)={sin}\left[\mathrm{2}\left(\frac{\mathrm{3}{x}}{\mathrm{2}}\right)\right] \\…

Given-a-sin-x-sin-2x-b-cos-x-cos-2x-If-a-2-b-2-a-2-b-2-3-cos-2x-3cos-x-then-x-

Question Number 129231 by liberty last updated on 14/Jan/21 $$\:\mathrm{Given}\:\begin{cases}{{a}=\mathrm{sin}\:{x}+\mathrm{sin}\:\mathrm{2}{x}}\\{{b}=\mathrm{cos}\:{x}+\mathrm{cos}\:\mathrm{2}{x}}\end{cases}.\:\mathrm{If}\:\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} −\mathrm{3}\right)=\mathrm{cos}\:\mathrm{2}{x}+\mathrm{3cos}\:{x} \\ $$$$\mathrm{then}\:{x}\:=? \\ $$ Answered by MJS_new last updated on 14/Jan/21…

y-x-dy-dx-a-y-2-dx-dy-

Question Number 129222 by bramlexs22 last updated on 14/Jan/21 $$\:\mathrm{y}−\mathrm{x}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{a}\left(\mathrm{y}^{\mathrm{2}} +\frac{\mathrm{dx}}{\mathrm{dy}}\:\right) \\ $$ Answered by bobhans last updated on 14/Jan/21 $$\:{y}−{xy}'\:=\:{ay}^{\mathrm{2}} +\frac{{a}}{{y}'} \\ $$$$\:{yy}'−{x}\left({y}'\right)^{\mathrm{2}} ={ay}^{\mathrm{2}}…

W-cos-5x-cos-4x-2cos-3x-1-dx-

Question Number 129223 by bramlexs22 last updated on 14/Jan/21 $$\:\mathrm{W}\:=\:\int\:\frac{\mathrm{cos}\:\mathrm{5x}+\mathrm{cos}\:\mathrm{4x}}{\mathrm{2cos}\:\mathrm{3x}−\mathrm{1}}\:\mathrm{dx}\: \\ $$ Answered by bobhans last updated on 14/Jan/21 $$\:{W}=\int\frac{\mathrm{2cos}\:\left(\frac{\mathrm{9}{x}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)}{\mathrm{2cos}\:\mathrm{3}{x}−\mathrm{1}}\:{dx} \\ $$$$\:{W}=\int\:\frac{\mathrm{2cos}\:\left(\frac{\mathrm{9}{x}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right).\mathrm{sin}\:\mathrm{3}{x}}{\mathrm{2cos}\:\mathrm{3}{x}\mathrm{sin}\:\mathrm{3}{x}−\mathrm{sin}\:\mathrm{3}{x}}\:{dx} \\ $$$$\:{W}=\:\int\:\frac{\mathrm{2cos}\:\left(\frac{\mathrm{9}{x}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)\mathrm{sin}\:\mathrm{3}{x}}{\mathrm{sin}\:\mathrm{6}{x}−\mathrm{sin}\:\mathrm{3}{x}}{dx} \\…