Question

How do you solve `tan^2x + secx = 1`?

Answer 1

tan^2x = sec^2x - 1#

`sec^2x - 1 + secx = 1`

`sec^2x + secx - 2 = 0`

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

`secx = -2 and secx = 1`

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

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

`x = 120˚ , 240˚ and 0˚`

Hopefully this helps!