Q. If $\sin^{x}{\alpha + \cos^{x}{\alpha \geq 1,0 < \alpha < \frac{\pi}{2},}}\$then
A) $x \in (2,\infty)$
B) $x \in ( - \infty,2\rbrack$
C) $x \in \lbrack - 1,1\rbrack$
D) None of these
Explanation
(b)
$\cos^{x}{\alpha + \sin^{x}{\alpha \geq 1}}$
Equality holds when $x = 2$
If $x < 2,$ both $\cos\alpha\$and${\ sin}\alpha$ are increasing
$\therefore\cos^{x}{\alpha + \sin^{x}{\alpha > 1,\ if\ x < 2}}$
If $x > 2,\$then${\ cos}^{x}{\alpha + \sin^{x}{\alpha < 1}}$
$\therefore x \in ( - \infty,2\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.