Question

`Sinx(1-cosx)^2+ cosx(1-sinx)^2=2` prove it?

Answer 1

The property you have asked of is false.

Explanation:

In order to disprove this relation, let `x=pi`. Our expression, denoted as `E(x)`, becomes:

`:. E(pi) = sinpi(1-cospi)^2+cospi(1-sinpi)^2`

`E(pi) =color(Red)0[1-(color(Red)(-1))]+(color(Red)(-1))(1-color(red)0)^2=0-1=-1`

Even if we do try to prove it, we will not reach a constant, but rather a function. In order to compensate for the identity being false, here are some alternative notations for `E(x)`:

`E(x)=(sinx+cosx)(1+cosxsinx)-4sinxcosx`
`E(x) = sinx+cosx + cosxsinx(sinx-4+cosx)`