Question

Please help, I'm so confused by this problem!
(cos x - sqrt 2/2)(sec x -1)=0
Part1: Use the zero product property to set up two equations that will lead to solutions to the original equation.

Part 2: Use a reciprocal identity to express the equation involving secant in terms of sine, cosine, or tangent.

Part 3: Solve each of the two equations in Part 1 for x, giving all solutions to the equation.

Answer 1

a*b = 0
either a = 0, b = 0 , or both a and b are = 0
so find out what will make the last happen to cover all bases
cos(x) - sqrt(2)/2 = 0
so
cos(x) = sqrt(2)/2

and

(sec x -1)=0
so
sec(x) = 1
1/cos(x) = 1
cos(x) = 1

Answer 2

you need to solve those two equations, can you do that?

Answer 3

there is going to be infinite solutions

Answer 4

Thank you so much! :D