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Given trigonometric identity :

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1 + sinx = cos²x / (1-sinx)

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Start from left hand side.

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1 + sinx

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 = (1 + sinx) / 1

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Rationalize with (1 - sinx)

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= (1 + sinx)(1 - sinx) / (1 - sinx)

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= (1² - sin²x) / (1 - sinx)

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= (1 - sin²x) / (1 - sinx)

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Substitute trigonometric identity : 1 - sin²x = cos²x

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= (cos²x) / (1 - sinx)

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Hence Trigonometric identity 1 + sinx = cos²x / (1-sinx) is proved.

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