Simplify [(sin(4a))/(1+cos(4a))] * [(cos(2a))/(1+cos(2a))]

Answer 1

sin4a/(1+cos4a) times cos2a/(1+cos2a) = tana

use double angle trig identities

sin2x = 2sinxcosx

cos2x= 2cos^2(x) -1

sin4a = 2sin(2a)cos(2a) = 2(2sinacos2a)(2cos^2(a)-1)

1+cos4a = 1+ 2cos^2(2a) -1 = 2cos^2(2a)

do some cancellations to get sina/cosa = tana

Answer 2

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