Question

Дано: 3sina + 3cosa = 1
Найдите: sin2A

Answer 1

3sin(a) + 3cos(a) = 1

3(sin(a) + cos(a)) = 1

sin(a) + cos(a) = 1/3

(sina + cosa)² = (1/3)²

sin²a +2sin(a)cos(a) + cos²a = 1/9

(sin²a + cos²a)+2sin(a)cos(a)  = 1/9

1+2sin(a)cos(a)  = 1/9

2sin(a)cos(a)  = 1/9 - 1

2sin(a)cos(a)  = sin(2a)  = - 8/9