given that sin (2x+30)=cos(x-15).determine the value of x given x is an acute angle

Answer 1

assuming that x is in degrees, then knowing that cos(x) = sin(90-x), we have

sin(2x+30) = sin(90-(x-15))
sin(2x+30) = sin(105-x)
so,
2x+30 = 105-x
3x = 75
x = 25

check:
sin(80) = cos(10)
yep.