- #1

- 804

- 37

## Homework Statement

4sec

^{2}θ tanθ = 8 tanθ

## Homework Equations

sec

^{2}θ = tan

^{2}θ + 1

## The Attempt at a Solution

4(tan

^{2}+ 1) tanθ = 8 tanθ

(4tan

^{2}+ 4) tanθ = 8 tanθ

4 tan

^{3}+ 4 tanθ = 8 tanθ

4 tan

^{3}- 4 tanθ = 0

4tanθ(tan

^{2}θ - 1) = 0

4tanθ = 0

tanθ = 0

tan

^{-1}(tanθ) = tan

^{-1}(0)

tan

^{-1}θ = 0, π

tan

^{2}θ - 1 = 0

(tanθ + 1)(tanθ - 1) = 0

tanθ + 1 = 0

tanθ = -1

tan

^{-1}tanθ = tan

^{-1}(-1)

tan

^{-1}θ = 3π/4, 7π/4

tanθ - 1 = 0

tanθ = 1

tan

^{-1}tanθ = tan

^{-1}(1)

tan

^{-1}θ = π/4, 5π/4