Question

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

Recuerda:

$(x + y)(x - y) = {x}^{2} - {y}^{2}$

$\sin {}^{2} (x) + \cos {}^{2} (x) = 1$

$\cot {}^{2} (x) = \csc {}^{2} (x) - 1$

....

$\frac{ \cot {}^{2} (x) }{ \csc(x) - 1} = \csc(x) + (1)$

$\cot {}^{2} (x) = (\csc(x) + 1)( \csc(x) - 1)$

$\cot {}^{2} (x) = \csc {}^{2} (x) - {1}^{2}$

$\cot {}^{2} (x) = \csc {}^{2} (x) - {1}^{}$

$\cot {}^{2} (x) = \cot {}^{2} (x)$

$1 = 1$

La expresion es verdadera.