Question

доказать тождество

cos4A-sin4A*ctg2A=-1

Answer 1

cos4a - sin4a*ctg2a = (cos2a)^2 - (sin2a)^2 - 2sin2a*cos2a*cos2a / sin2a =

(cos2a)^2 - (sin2a)^2 - 2(cos2a)^2 = -((sin2a)^2 + 2(cos2a)^2) = -1