How do i demonstrate that there is only one value of x (between 0 and 2pi) that verifies cosx=3/5 and sinx=4/5

well, as we can see, the cos(x) as well as the sin(x) are both positive, that puts the angle in the I Quadrant only, everywhere else they differ in signs or are both negative.

that simply means it has an adjacent side of 3, opposite side of 4, and a hypotenuse of 5, like you see it in the picture below.

and we can get the inverse function of either function to get about 53.130102354° for ∡x.

nada

step-by-step explanation: