trig Q help plz?

Question

find in terms of (PI) the solution for:
sin5x + six = 0

i have worked it dwn to this step by using the 'factor formula'..
2sin3xcos2x=0
now i dnt kno how to simply it..can sum1 help plz..thnxs!

Answer 1

sin(5x) + sin(x) = 0
Using trigonometric identities:
2sin(3x)cos(2x) = 0
sin(3x)cos(2x) = 0

sin(3x) = 0
3x = nπ
x = nπ/3

OR
cos(2x) = 0
2x = (2n+1)π/2
x = (2n+1)π/4

x = {nπ/3, (2n+1)π/4} where n is an integer

Answer 2

try using this formula sina + sinb = 2sin((a+b)/2)cos((a-b)/2)

2sin((5x+x)/2)cos((5x-x)/2) = 0

sin3x = 0 x = 0 or pi/3
cos2x = 0 x = pi/4

Answer 3

I'm ******* glad i'm not in trigonometry.