If 0≤x≤π/2 and 81sin2⁡x+81cos2⁡x=30, then x is equal

A
$\frac{π}{6}, \frac{π}{3}$
B
$\frac{π}{3}, \frac{5 π}{2}$
C
$\frac{5 π}{6}, \frac{π}{6}$
D
$\frac{2 π}{3}, \frac{π}{3}$

Solution:

Let $81^{\sin^{2} x} = y$ Than,

$81^{\cos^{2} x} = 81^{1 - \sin^{2} x} = 81 y^{- 1}$

$\begin{array}{l} \Rightarrow 81^{\sin^{2} x} + 51^{\cos^{2} x} = 30 \\ \Rightarrow y + 81 y^{- 1} = 30 \\ \Rightarrow y^{2} - 30 y + 81 = 0 \\ \Rightarrow y = 3 or, y = 27 . \\ \Rightarrow 81^{\sin^{2} x} = 3 or, 27 \\ \Rightarrow 3^{4 \sin^{2} x} = 3^{1} or, 3^{3} \\ \Rightarrow 4 \sin^{2} x = 1 or, 3 \\ \Rightarrow \sin^{2} x = \frac{1}{4} or, \frac{3}{4} \\ \Rightarrow \sin x = \pm \frac{1}{2} or, \pm \frac{\sqrt{3}}{2} \Rightarrow x = \frac{π}{6} or, \frac{π}{3} \end{array}$

If $0 \leq x \leq π / 2$ and $81^{\sin^{2} x} + 81^{\cos^{2} x} = 30$ , then $x$ is equal

Solution:

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