Solve tan x - 1 = 0 for all values of x.

Answer 1

tan x - 1 = 0

tan x = 1

When does the tangent of an angle equal 1? Hmm...

We can re-write tan x

(sin x)/(cos x) = 1

When does a fraction equal 1?

sin x = cos x

Now, if you imagine the unit circle, you will remember that sin θ gives y-coordinates on your circle and cos θ gives x-coordinates on your circle. For this question, we need to figure out the values of our angle such that the y-coordinate on our unit circle equals the x-coordinate on our unit circle.

x = {π/4 + πk, k ∈ ℤ}