Question

${\sin }^{2n}x+{\cos }^{2n}x$ lies between

• A. $-1$ and $1$
• B. $0$ and $1$
• C. $1$ and $2$
• D. none of these

Answer 1

The correct option is B $0$ and $1$

${\sin }^{2n}x+{\cos }^{2n}x$

Since the functions are comprised by even powers The min value is $0$

The max value is $1$ since square of values less than $1$ are even less than $1$

So The rangle is $[0,1]$