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Prove that $\frac{(\sin{A}+\sin{3A})}{(\cos{A}+\cos{3A})}=\tan{2A} $
in Grade 12 Maths by Diamond (40.1k points) | 19 views

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LHS:

(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, proven.
by Silver Status (31.3k points)

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