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

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

1 Answer

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Answer 1 · 2015-12-07T03:15:27

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

Explanation:

$\frac{{cos}^{2} x}{{sin}^{2} x} + \frac{1}{{sin}^{2} x} = \frac{{cos}^{2} x + 1}{{sin}^{2} x} =$ $cos^2 x/(sin^2 x) + 1/(sin^2 x) = (cos^2 x + 1)/(sin^2 x) =$
$= \frac{1 - {sin}^{2} x + 1}{{sin}^{2} x} = \frac{2 - {sin}^{2} x}{{sin}^{2} x} =$ $= (1 - sin^2 x + 1)/(sin^2 x) = (2 - sin^2 x)/(sin^2 x) =$
$= \frac{2}{{sin}^{2} x} - \frac{{sin}^{2} x}{{sin}^{2} x} = 2 {csc}^{2} x - 1$ $= 2/(sin^2 x) - sin^2 x/(sin^2 x) = 2csc^2 x - 1$

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

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Explanation:

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How do you prove that cot2x+csc2x=2csc2x−1 cot^2 x +csc^2 x = 2csc^2 x - 1 ?

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Explanation:

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