Question

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

Answer 1

I tried changing `tan` into `sin and cos`:

Explanation:

You can change the tangent as:
`tan(x)=sin(x)/cos(x)` and write it as:
`1+1/(sin^2(x)/cos^2(x))=1/sin^2(x)`
rearranging the left side:
`1+cos^2(x)/sin^2(x)=1/sin^2(x)`
`(sin^2(x)+cos^2(x))/sin^2(x)=1/sin^2(x)`
but: `sin^2(x)+cos^2(x)=1`
so:
`1/sin^2(x)=1/sin^2(x)`