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$The maximum value of y = \frac{1}{\sin^{6} x + \cos^{6} x}$

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Correct option is A

We havesin6x+cos6x=1-3sin2xcos2x =1-34sin22x⇒1sin6x+cos6x=44-3sin22x∴ymax=44-3(1)=4

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The maximum value of y=1sin6x+cos6x

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$The maximum value of y = \frac{1}{\sin^{6} x + \cos^{6} x}$