a sin x + b cos x = cos(x-60), maka a + b akar 3 =

jawab
a sin x + b cos x = k cos ( x- 60)

a² + b² = k²
a² + b² = 1 ...(i)

tan 60 = b/a
1/√3 = b/a
a = b√3 ...(ii)

ii sub ke i
(b√3)² + b² = 1
3b² + b² = 1
4b² = 1
b= 1/2 

a = b√3
a = 1/2 √3

a + b√3 =  1/2 √3 + 1/2 √3
a + b√3= √3