Question

Докажите тождество : (альфа заменила на a) a)sin a + sin3a + sin5a + sin7a = 4cos a *cos2a* sin 4a b) sin^2 a * cos^2 a = 1/8 - 1/8 cos4a

Answer 1

b)  1/8 - 1/8 cos4a = 1/8(1-cos4a) = 1/8*2sin^2 2a = 1/4sin^2 2a = 1/4*(2sina*cosa)^2 = sin^2 a * cos^2 a

a) sin a + sin3a + sin5a + sin7a = 2sin4a*cosa+2sin4a*cos3a = 2sin4a*(cosa+cos3a) = 2sin4a*2cos2a*cosa = 4cos a *cos2a* sin 4a