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28 May 2019

Prove that, (sinA+sin3A)/(cosA+cos3A) = tan2A

Prove that,  (sinA+sin3A)/(cosA+cos3A) = tan2A

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Sol. Now,  
(sinA+sin3A)/(cosA+cos3A)
= (sinA+3sinA-4sin^3A)/(cosA+4cos^3A-3cosA)
 = (4sinA-4sin^3A)/(4cos^3A-2cosA)
 = [4sinA(1-sin^2A)]/[2cosA(2cos^2A-1)]
 = (4sinAcos^2A)/(2cosAcos2A)
 = (2sinAcosA)/cos2A
 = sin2A/cos2A
 = tan2A


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