sin(2x)=1/2

let b=2x

values of b that give +1/2 are 30 and 150

so sinb=1/2 where b =30,150

b=2x implies 2x=30 and 2x = 150

sin^2 x =1/2 is the same as (sinx)^1/2 =1/2,

thus sinx = sqrt(1/2)

values of x that give +1/sqrt(2) are 45 and 135

cos(x-30)=1

let x-30=b

so cosb=1

values of b that give +1 are 0 and 360

this means x-30=0 and x-30=360

cos^2 x =3/2

this is the same as cosx=sqrt(3/2)

but sqrt(3/2) is > than 1.

cosx has a range of 1>y>-1

so there is no solution