Question

Solve the equation algebraically, and then use a calculator to find the values on the interval [0, 2π). (Enter your answers as a comma-separated list. Round your answers to four decimal places.)

$tan^2(x)-sec(x)=1$

I don't know what other radians I left out... any help is very much appreciated thank you.

Answer 1

Answer:

pi/3, pi, 2pi/3

Step-by-step explanation:

1+tan²x = sec²x

sec²x - 1 - secx -1 = 0

sec²x- secx - 2 = 0

sec²x - 2secx + secx - 2 = 0

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

secx = -1

cosx = -1

x = pi

secx = 2

cosx = ½

x = pi/3, 5pi/3