The expression sin^{2n}x + cos^{2n}x lies bet | vedclass

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(A) We know that for $n \geq 1$ and $x \in \mathbb{R}$,$0 \leq \sin^2 x \leq 1$ and $0 \leq \cos^2 x \leq 1$.Since $0 \leq \sin^2 x \leq 1$,it follows

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$0$ and $1$

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(A) We know that for $n \geq 1$ and $x \in \mathbb{R}$,$0 \leq \sin^2 x \leq 1$ and $0 \leq \cos^2 x \leq 1$.Since $0 \leq \sin^2 x \leq 1$,it follows that $0 \leq \sin^{2n} x \leq \sin^2 x$.Similarly,$0 \leq \cos^{2n} x \leq \cos^2 x$.Adding these inequalities,we get $0 \leq \sin^{2n} x + \cos^{2n} x \leq \sin^2 x + \cos^2 x$.Since $\sin^2 x + \cos^2 x = 1$,we have $0 Specifically,the minimum value is $1/2^{n-1}$ (at $x = \pi/4$) and the maximum value is $1$ (at $x = 0$ or $x = \pi/2$).

The expression $sin^{2n}x + cos^{2n}x$ lies between which of the following values?

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