Question

tga 

tga+ctga    = cos2a

Answer 1

tga/(tga+ctga) = cos^2 a
tga/(sin^2 a + cos^2 a)/sina*cosa = cos^2 a
sina/cosa * sina*cosa = cos^2 a
sin^2 a = cos^2 a
sin^2 a - cos^2 a = 0
-(cos^2 a - sin^2 a) = 0
cos2a = 0
2a = p/2 + pk
a = p/4 + pk/2