Question

Pruebalo `(sinx-cosx)^2=1-1/csc^2x`?

Answer 1

`(sinx-cosx)^2=1-1/csc(2x)`

Explanation:

The question appears to be in Spanish and I am answering in English. I hope answer will satisfy you.

`(sinx-cosx)^2` - using `(a-b)^2=a^2+b^2-2ab`, we get

= `sin^2x+cos^2x-2sinxcosx`

= `1-sin2x` - (as `sin^2x+cos^2x=1` and `sin2x=2sinxcosx`)

= `1-1/csc(2x)` - as `sinA=1/cscA`

Note `(sinx-cosx)^2=1-1/csc(2x)` and not `1-1/csc^2x` as

`1-1/csc^2x=1-sin^2x=cos^2x`