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

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