First slide

Trigonometric Identities

Question

$If \sin^{x} α + \cos^{x} α \geq 1, 0 < α < \frac{π}{2}, then$

Moderate

A

$x \in [2, \infty)$
B

$x \in (- \infty, 2]$
C

$x \in [- 1, 1]$
D

$x \in ℝ$

Solution

[SolutionStep1]:
$\sin^{x} α + \cos^{x} α \geq 1, 0 < α < \frac{π}{2}$
$Since equality holds for x = 2$
$If x < 2, both \cos α and \sin α increase (being + ve fraction).$
$\cos^{x} α + \sin^{x} α > 1 if x < 2$
$Thus x \leq 2 i.e. x \in (- \infty, 2]$

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