Question

$f\left(x\right)=1$ and $\varphi \left(x\right)={\sin }^{2}x+{\cos }^{2}x.$
Show that both functions are equal?

Answer 1

$f\left(x\right)=1\forall x\in R$
And $\varphi \left(x\right)={\sin }^{2}x+{\cos }^{2}x=1\forall x\in R$
Hence $f\left(x\right)$ and $\varphi \left(x\right)$ are identical (equal) function.
Since both function have same domain and range.