Question

prove that tan^2A+Cot^2A =1 is not a trigonometric identity by producing a counterexample

Answer 1

tan^2A+Cot^2A ≠ 1

For example

Tan 30= √3/3

Cotan 30= √3

Then

Tan^2 30 = (√3/3)^2 = 3/9= 1/3

Cotan^2 30 = (√3)^2 = 3

So then, adding both results

Tan^2 30 + Cotan^2 30 = 1/3 + 3 = 10/3

SO WE SEE THAT 10/3 ≠ 1