Вычислите: sin(arccos (-4/5) + arcsin 1/3)

Question

Вычислите: sin(arccos (-4/5) + arcsin 1/3)

Answer 1

u = arccos (- 4/5)

v = arcsin 1/3

sin(u + v) = sin(arccos (- 4/5)).cos(arcsin 1/3) + cos(arccos (- 4/5)).sin(arcsin (1/3)) =

=  √[1 – (- 4/5)²] * √[1 – (1/3)²]   + (- 4/5)*(1/3) = √[1 – 16/25] * √[1 – 1/9]   - 4/15 = 

 = √[(9/25)*(8/9)] – 4/15 = (2√2) / 5 - 4/15 = (6√2 - 4) / 15