what is the solution of y=cos^2(4x+b)

Answer 1

here it is, with b=3

https://www.wolframalpha.com/input/?i=y%3Dcos%5E2%284x%2B3%29+

Now, if you want to find x where y=0, then you need
4x+b = π/2 + kπ
so
x = ((k+1)/2 π - b)/4