Question

How do you verify `(sin(x)+cos(x))^2=1+sin^2(x)`?

Answer 1

I think it is not true.

Explanation:

You can write it as:
`sin^2(x)+2sin(x)cos(x)+cos^2(x)=sin^2(x)+cos^2(x)+sin^2(x)`
where you used the fact that:
`1=sin^2(x)+cos^2(x)`
so:
`cancel(sin^2(x))+2sin(x)cos(x)+cancel(cos^2(x))=cancel(sin^2(x))+cancel(cos^2(x))+sin^2(x)`
and:
`2sin(x)cos(x)=sin^2(x)` Not true