Question

How do you prove `1+1/tan^2x = 1/sin^2x`?

Answer 1

Know that:

`cot^2x=1/tan^2x`

And also that:

`sin^2x+cos^2x=1`

`sin^2x/sin^2x+cos^2x/sin^2x=1/sin^2x`

`1+cot^2x=1/sin^2x`

Therefore:

`LHS`

`=1+1/tan^2x`

`=1+cot^2x`

`=1/sin^2x`

`=RHS`