Find all real numbers that satisfy the equation cos 4 beta

Find all real numbers that satisfy the equation cos (4 beta) = 1 Use the smallest nonnegative arcs for the solution set Select the correct answer below, and if necessary, fill in the answer box to complete your choice a. The solution {beta | beta} where k is any integer (Type an expression using k as the variable Type your answer in radians Type an exact answer, using pi as needed. Use integers or fractions for any numbers in the expression.) There is no solution

Solution

We have given cos(4)=1

when 4=0+2pi*k then cos(4)=1

=0+(1/2)*(pi*k)

when 4=2pi+2pi*k then cos(4)=1

=pi/2 +(1/2)*(pi*k)

The solution set is {| =(0+(1/2)*(pi*k),pi/2 +(1/2)*(pi*k))} for any integer k and 2pi is the period of cosine

answer is A