Question

How do you simplify `(1+tan^2x)/(1+cot^2x)`?

Answer 1

`tan^2x`

Explanation:

`(1+tan^2x)/(1+cot^2x)`

1) First, notice that both the numerator and denominator are Pythagorean Identities. Proceed to change them.

`sec^2x/csc^2x`

2) Turn into sine and cosine. Then multiply.

`(1/cos^2x)/(1/sin^2x)` `->` `1/cos^2x * sin^2x/1` `->` `tan^2x`

:)