Solve sec2(theta) = sec(theta) + 2 using exact values over

Question

a. the domain -2pi ≤ x < 2pi

b. the real numbers

Answer 1

Let U = sec(t)

U^2 = U +2

U^2 -U - 2 = 0

( U - 2 )( U + 1 ) = 0

U = 2 or U = -1

secant is 2 or secant is -1

cosine is 1/2 or cosine is -1

cosine is 1/2 at degrees of 60,120

or pi/3 and 2*pi/3

cosine is -1 at 180 degrees or pi

pi/3 + 2*k*pi or 2*pi/3 + 2*k*pi

or pi*2*k

for integer k