If $s i n x + c o s e c x = 2, t h e n s i n^{n} x + c o s e c^{n} x$ is equal to

2

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2^{n}

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2^{n - 1}

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2^{n - 2}

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Solution

The correct option is A $2$
$s i n x + c o s e c x = 2 \Rightarrow (s i n x - 1)^{2} = 0 \Rightarrow s i n x = 1$
$∴ s i n^{n} x + c o s e c^{n} x = 1 + 1 = 2.$

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