Using intermediate value theorem, prove that there exists a number $x$ such that $x^{2005} + \frac{1}{1 + sin ^{2} x} = 2005 .$

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Using intermediate value theorem, prove that there exists a number

x

such that

x^{2005} + \frac{1}{1 + sin ^{2} x} = 2005 .

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Question Text

Using intermediate value theorem, prove that there exists a number

x

such that

x^{2005} + \frac{1}{1 + sin ^{2} x} = 2005 .

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