Доказать тождество sin5a-sin3a если sin a=3 / √5

Sin5a-sin3a=2sinacos4a=2sinacos (3a+a) = 2sina * (4 (cos^4a+sin^4a) - 3)) =

=8sina * (cos^4a+sin^4a) - 6sina

cos4a=cos (3a+a) = cos3acosa-sin3asina=cosa (4cos³a-3cosa) - sina (3sina-4sin³a) =

=4coa^4a-3cos²a-3sin²a+4sin^4a=4 (cos^4a+sin^4a) - 3 (sin²a+cos²a) = 4 (cos^4a+sin^4a) - 3