Prove or disprove the following identity:

Question

cos (x+pi/6) +sin (x-pi/3) = 0

Answer 1

I will use 30° and 60° , easier to type
cos (x+300) +sin (x-60)
= cosxcos30 - sinxsin30 + sinxcos60 - cosxsin60
= (√3/2)cosx - (1/2)sinx + (1/2)sinx - (√3/2)cosx
= 0
= RS