Solve for the x in interval [0,2π) Sec^2 x=4

Answer 1

Solve for the x in interval [0,2π) Sec²x=4.

You need first the reciprocal identity:

sec(x) = 1/cos(x)

1/cos²x = 4

1/4 = cos²x

Get the square root of both sides of the equation:

cos x = ±1/2

For cos x=1/2

x = π/3, 5π/3

For cos x = -1/2

x = 2π/3, 4π/3