Question

Problems using domain and range of trigonometric ratios $(\sin ,\cos ,\tan )$. Range of $f\left(x\right)={\sin }^{20}x+{\cos }^{48}x$ is?

Answer 1

$0\le {\sin }^{2n}\theta \le 1;0\le {\cos }^{2k}\theta \le 1$

$\therefore$ $0\le f\left(x\right)={\sin }^{20}x+{\cos }^{48}x\le 1$