Final answer:
To find the exact solutions of the equation sqrt(2) cos(x)-1=0, isolate the cosine function and solve it by considering the unit circle and the values of cosine for certain angles.
Step-by-step explanation:
To find the exact solutions of the equation sqrt(2) cos(x)-1=0, we can isolate the cosine function and then solve it. First, add 1 to both sides of the equation to get sqrt(2) cos(x)=1. Then, divide both sides by sqrt(2) to obtain cos(x)=1/sqrt(2). The exact solutions of this equation can be found by considering the unit circle and the values of cosine for certain angles. One such angle is pi/4, which corresponds to cos(pi/4)=1/sqrt(2). Another angle is 7pi/4, which also gives cos(7pi/4)=1/sqrt(2). Therefore, the exact solutions of the equation are x=pi/4+2npi and x=7pi/4+2npi, where n is an integer.