Trigonometry HELP PLEASE

Question

If sin(2x+12) = cos(4x-6), then solve for x on the interval [0,180)

Answer 1

Using the identity of cos(y)= sin(90-y)

we can rewrite as

sin(2x+12)=sin(90-(4x-6))

so therefore we have

2x+12=90-4x+6

so solving we have

6x=84

so x=14

 

checking we have sin(40)=cos (50)

which checks.