solve the equation on the interval 0≤θ<2π

Question

secθ=tanθ+cotθ

Answer 1

sometimes it helps to convert everything to sines and cosines

let s = sinx and c = cosine x.

secx = 1/c

tanx = s/c

cotx = c/s

secx = tanx + cotx

1/c = s/c + c/s

multiply both sides by cs

s = s^2 + c^2 = 1

s = 1

sinx = 1

x = sin^-1(1)

x = 90 degrees + 360n where n = any integer

or

x = pi/2 + 2npi where n = any integer