Start with multiplying given equation by 2. Result is:
2 sinx cosx = 1
Now use well known trigonometric identity, sin2x=2sinxcosx, to obtain:
sin 2x = 1
To solve this equation, we take a look at trigonometric table and find angles θ that give sin θ = 1.
All solutions to the equation are:
2x=π2+2kπ, where k∈Z
x=π4+kπ, where k∈Z