Solve for all the values of x. Give the answer in radians

Question

Solve for all the values of x. Give the answer in radians

5 sec^2 theta - 20 = 0 ( theta)

Answer 1

5Sec²Θ -20 = 0

Sec²Θ = 4

1/Cos²Θ = 4

Cos²Θ = 1/4 = 0.25

Take square root of both sides:

CosΘ = 0.5

Θ = Π/3

Answer 2

5sec^2x-20=0

sec^2x-4=0

(secx-2)(secx+2)=0

secx=2

secx=-2

sec=1/cos

1/cos=2, therefore cos=1/2

1/cos=-2, therefore cos=-1/2

cosx=1/2 and cosx=-1/2

look on the unit circle

cosx=1/2 when x=∏/3 and x=5∏/3

cosx=-1/2 when x=2∏/3 and x=4∏/3

x=∏/3, 2∏/3, 4∏/3 and 5∏/3