Вычислите sin 2a, cos 2b, sin (a-b), cos (a+b), если sin a=4/5, cos b = - 5/13

1) Т. к. sin²2a+cos²2a=1, то

sin2a=√ (1-cos²2a).

А также cos2a=1-2sin²a, то

sin2a=√ (1 - (1-2sin²a) ²) = √ (1 - (-7/25) ²) = √ (576/625) = 24/25.

2) cos2b=2cos²b - 1 = - 119/169.

3) sin (a-b) = sinacosb-cosasinb=

=-4/13-√ (1-sin²a) (1-cos²b) =

=-4/13-√ (9/25) (144/169) = - 4/13 - (3/5) (12/13) = - 56/65.

4) cos (a+b) = cosacosb-sinasinb=-5/13√ (1-sin²a) - 4/5√ (1-cos²b) = (-5/13) (3/5) - (4/5) (12/13) = - 63/65.