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Question Number 42520 by gyugfeet last updated on 27/Aug/18

cos^3  A.sin3A+sinA.cos3A=(3/4)sin4A

$${cos}^{\mathrm{3}} \:{A}.{sin}\mathrm{3}{A}+{sinA}.{cos}\mathrm{3}{A}=\frac{\mathrm{3}}{\mathrm{4}}{sin}\mathrm{4}{A} \\ $$

Answered by tanmay.chaudhury50@gmail.com last updated on 27/Aug/18

cos3A=((4cos^3 A−3cosA)/)  (((3cosA+cos3A)/4))sin3A+sinAcos3A  ((3cosAsin3A+cos3Asin3A+4sinAcos3A)/4)  ((3(cosAsin3A+sinAcos3A)+cos3Asin3A+sinAcos3A)/4)  ((3sin4A+cos3A(sin3A+sinA))/4)  (3/4)sin4A+(1/4)cos3A(2sin2AcosA)  pls check the auestion...

$${cos}\mathrm{3}{A}=\frac{\mathrm{4}{cos}^{\mathrm{3}} {A}−\mathrm{3}{cosA}}{} \\ $$$$\left(\frac{\mathrm{3}{cosA}+{cos}\mathrm{3}{A}}{\mathrm{4}}\right){sin}\mathrm{3}{A}+{sinAcos}\mathrm{3}{A} \\ $$$$\frac{\mathrm{3}{cosAsin}\mathrm{3}{A}+{cos}\mathrm{3}{Asin}\mathrm{3}{A}+\mathrm{4}{sinAcos}\mathrm{3}{A}}{\mathrm{4}} \\ $$$$\frac{\mathrm{3}\left({cosAsin}\mathrm{3}{A}+{sinAcos}\mathrm{3}{A}\right)+{cos}\mathrm{3}{Asin}\mathrm{3}{A}+{sinAcos}\mathrm{3}{A}}{\mathrm{4}} \\ $$$$\frac{\mathrm{3}{sin}\mathrm{4}{A}+{cos}\mathrm{3}{A}\left({sin}\mathrm{3}{A}+{sinA}\right)}{\mathrm{4}} \\ $$$$\frac{\mathrm{3}}{\mathrm{4}}{sin}\mathrm{4}{A}+\frac{\mathrm{1}}{\mathrm{4}}{cos}\mathrm{3}{A}\left(\mathrm{2}{sin}\mathrm{2}{AcosA}\right) \\ $$$${pls}\:{check}\:{the}\:{auestion}... \\ $$

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