sin2x=cos(x+30)

Question

Solve for X in trigonomatry

Answer 1

sin(2x)=cos(x+30),

cos(90-2x)=cos(x+30),

90-2x=x+30,

60=3x, x=20° is one solution but there are many others.

sin(2x)=sin(360n+2x) where n is an integer.

So cos(90-360n-2x)=cos(x+30),

90-360n-2x=x+30,

90-30-360n=3x, 

60-360n=3x,

x=20-120n. This can also be written x=20+120n since n is an arbitrary integer.

x= 20, 140, 260, 380, ... degrees.

Also, cos(-x-30)=cos(x+30), so:

90-360n-2x=-x-30,

120-360n=x which can be written x=120+360n,

x=120, 480, 840, ... degrees.