#1**+2 **

cos(A - 90°) = cos(A)cos(90°) + sin(A)sin(90°) or cos(A - 90°) = cos(A)*0 + sin(A)*1 or cos(A - 90°) = sin(A)

If A = x + 34, then sin(x + 34) can be written as cos(x + 34 - 90) or cos(x - 56)

So if sin(x+34) = cos(2x + 20) we could also write cos(x - 56) = cos(2x + 20) which means that x - 56 = 2x + 20

rearranging, we have: x = -76°

Check:

sin(-76+34) = -0.6691

cos(2*(-76)+20) = -0.6691

If you want a value of x between 0 and 360, simply add 360 to x (i.e 360 - 76 = 284).

Alan Mar 28, 2018