Question

Let $f\left(x\right)={\sin }^{2}x+{\cos }^{2}x,g\left(x\right)=1$

$f\left(x\right)$ and $g\left(x\right)$ are identical

• A. True
• B. False

Answer 1

The correct option is A

True

For two functions to be identical or equal, both the functions should have the same range and same domain.

So we will find the range and domain of the functions given.

$f\left(x\right)={\sin }^{2}x+{\cos }^{2}x=1$, for all $x\in R$ .

The domain and range of both the functions are equal

$\Rightarrow$ They are identical

Range = {1}

Domain = R (set of all real numbers)