Question

$A={\sin }^8\theta +{\cos }^{14}\theta$, then for all values of $\theta$

• A. $A\le 1$
• B. $1<2A\le 3$
• C. $A\ge 1$
• D. $0\le A\le \frac{1}{2}$

Answer 1

The correct option is A $A\le 1$

$si{n}^8\theta \le si{n}^2\theta -------------------------\left(1\right)$

$co{s}^{14}\theta \le co{s}^2\theta ------------------------\left(2\right)$

Adding equation (1) and (2):

$A\le 1$