Question

The number of principal solutions of tan 2θ = 1 is ______.

Options

• one

• two

• three

• four

Answer 1

The number of principal solutions of tan 2θ = 1 is two.

Explanation:

We have, tan 2θ = 1.

`implies` tan 2θ = `tan  π/4`.

`implies` 2θ = `nπ + π/4`.

`implies` θ = `n/2 π + π/8`.

Also, the value of tan 2θ is positive.

So, θ lies in 1st and 3rd quadrants.

∴ θ = `π/8` and `(9π)/8`, are the two principal solutions.