Question
Find general solution of
sin(pi-6x)+root 3 sin((pi/2) +6x))=root3
sin(pi-6x)+root 3 sin((pi/2) +6x))=root3
Answers
oobleck
sin(π-6x) = sin6x
sin(π/2 + 6x) = cos6x
so now you have
sin6x + √3 cos6x = √3
√3/2 cos6x + 1/2 sin6x = √3/2
cos(6x - π/2) = √3/2
6x - π/2 = π/6 or -π/6
6x = (2π/3 or π/3) + 2kπ
x = (π/9 or π/18) +kπ/3
sin(π/2 + 6x) = cos6x
so now you have
sin6x + √3 cos6x = √3
√3/2 cos6x + 1/2 sin6x = √3/2
cos(6x - π/2) = √3/2
6x - π/2 = π/6 or -π/6
6x = (2π/3 or π/3) + 2kπ
x = (π/9 or π/18) +kπ/3