Question

Range of the function $f\left(x\right)={\sin }^{20}x+{\cos }^{48}x$ is

• A. $[0,1]$
• B. $(0,1]$
• C. $(0,\infty )$
• D. $(-\infty ,0)$

Answer 1

The correct option is B $(0,1]$

If $0\le a\le 1$ then $a^2\le a$, so we use that repetadly

$A=si{n}^{20}x+co{s}^{48}x\le {\sin }^{2}x+co{s}^{2}x=1$

So $Amax=1$ and it is achieved at $x=0$

Therefore the range of function is,

$(0,1]$