What is the value of X if SIN(X) - COS(X)= pie/6?

Answer 1

we must try to find a and b
so sinx-cos x= a cos(x+b) = a cos b cos x -a sin b sin x
a cos b =-1
-a sin b = 1
squaring both sides and summing a^2=2 so a=sqrt2(We take the positive solution)
tan b= 1 so b= 5pi/4 as cos b and sin b<0
so sqrt2*cos( x+5pi/4))= pi/6
cos(x+5pi/4)= 0.3702 and x= -2,7355+2kpi and
x=-5.1185 +2kpi (k any integer)

Answer 2

x = 66.73°