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cos 2 A = 2 cos² A - 1 = 4/5
cos² A =1/2 ( 4/5 + 1) = 9/10
cos A = √(9/10)= 3/10 √10
cos 2 A = 1 - 2sin² A
4/5 = 1 - 2 sin² A
2 sin² A = 1 - 4/5 = 1/5
sin² A = 1/10
sin A = √(1/10) = 1/10 √10
tan A = sin A /cos A = (1/10 √10) / (3/10 √10) = 1/10 : 3/10= 1/3