Question

Find all solutions and write the answer in a general form. 6 sec2(x) − 6 = 0

Answer 1

x = pi n

Explanation:

6 sec^2(x) − 6 = 0

Add 6 to each side

6 sec^2(x) − 6+6 = 0+6

6 sec^2(x)=6

Divide by 6

sec^2(x) = 1

Take the square root of each side

sqrt( sec^2(x) ) = ±sqrt(1)

sec(x) =± 1

sec (x) = 1 sec(x) = -1

Take the inverse sec of each side

sec^-1(sec (x)) = sec^-1(1) sec^-1(sec (x)) = sec^-1(-1)

x = 2 pi n x = pi + 2 pi n where n is an integer

Combining

x = pi n