jika sin a - sin b = 3/5 dan cos a + cos b = 4/5, maka sin ( a + b )

jawab

sin a - sin b  =  3/5
cos a + cos b = 4/5

(sin a - sin b)² + (cos a + cos b)²  = (3/5)²+ (4/5)² = 9/25 +16/25 = 1
(sin² a + sin² b - 2 sin a sin b + cos² a + cos² b + 2 cos a cos b = 1
{ (sin² a+ cos² a )+ (sin² b + cos ² b)  - 2 sin a sin  b + 2 cos a cos b} = 1
( 1 + 1  - 2 sin a cos a + 2 cos a cos b) = 1
- 2 sin a sin b+ 2 cos a cos b = 1- 2 = - 1
-2 { cos a cos b - sin a sin b } = - 1
cos a cos b - sin a sin b =  -1/ -2
cos (a + b) = 1/2

sin (a + b) = √ (1 - cos² (a+b)) = √ (1 - (1/2)²)= √(1 - 1/4) = √(3/4)
sin (a + b) =  1/2 √3