If 0≤x≤π,81sin2x+81cos2x=30 then x =

If81sin2x=y⇒81cos2x=81y∴y+81y=30⇒y2−30y+81=0⇒y=27,3

If 0≤x≤π,81sin2x+81cos2x=30 then x =

If81sin2x=y⇒81cos2x=81y∴y+81y=30⇒y2−30y+81=0⇒y=27,3

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

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$\frac{π}{6}$

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$\frac{π}{8}$

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$I f 81^{\sin^{2} x} = y \Rightarrow 81^{\cos^{2} x} = \frac{81}{y}$

$∴ y + \frac{81}{y} = 30 \Rightarrow y^{2} - 30 y + 81 = 0$

$\Rightarrow y = 27, 3$

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