Question

If `tan θ + 1/tan θ = 2`, find the value of `tan^2 θ + 1/(tan^2 θ)`.

Answer 1

Given:

`tan θ + 1/tan θ = 2`

Squaring both sides:

`(tan θ + 1/tan θ)^2 = 2^2`

`tan^2 θ + 1/(tan^2 θ) + 2(tan θ) (1/tan θ) = 4`

`tan^2 θ + 1/(tan^2θ) + 2 = 4`

`tan^2 θ + 1/(tan^2 θ) = 4 - 2`

`tan^2 θ + 1/(tan^2 θ) = 2`