Solve for x if sin2x=cos(x+60 and x€ [-90,180].show all work details

Answer 1

What does x€ [-90,180] mean?
The domain limits of x?

You seem to have omitted a parenth after x+60

cos(x+60) = sin(90-x-60)
= sin (30-x)

sin2x = sin(30-x)

Therefore 2x = 30 -x
x = 10 degrees is one solution

See if you can find others. Note that sin2x = sin(180 -2x); that will lead to another solution.

Answer 2

Yes it mean domaim limit of x that guied u when plot the graph