How do you prove that $cot^2 x +csc^2 x = 2csc^2 x - 1$ ?

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How do you prove that $cot^2 x +csc^2 x = 2csc^2 x - 1$ ?

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Answer 1 · 2015-12-07T03:15:27

Prove: $cot^2 x + csc^2 x = 2csc^2 x - 1$

Explanation:

$cos^2 x/(sin^2 x) + 1/(sin^2 x) = (cos^2 x + 1)/(sin^2 x) =$
$= (1 - sin^2 x + 1)/(sin^2 x) = (2 - sin^2 x)/(sin^2 x) =$
$= 2/(sin^2 x) - sin^2 x/(sin^2 x) = 2csc^2 x - 1$

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How do you prove that $cot^2 x +csc^2 x = 2csc^2 x - 1$ ?

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How do you prove that cot^2 x +csc^2 x = 2csc^2 x - 1 cot^2 x +csc^2 x = 2csc^2 x - 1 ?

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How do you prove that $cot^2 x +csc^2 x = 2csc^2 x - 1$ ?