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

# If $0\le x\le \pi /2$ and ${81}^{{\mathrm{sin}}^{2}x}+{81}^{{\mathrm{cos}}^{2}x}=30$, then is equal

1. A

$\frac{\pi }{6},\frac{\pi }{3}$

2. B

$\frac{\pi }{3},\frac{5\pi }{2}$

3. C

$\frac{5\pi }{6},\frac{\pi }{6}$

4. D

$\frac{2\pi }{3},\frac{\pi }{3}$

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### Solution:

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

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

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