Question

Show that cotA*cotB+cotB*cotC+cotC*cotA=1, if A+ B +C=π
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Answer 1

$a + b = \pi - c$

$\cot(a + b) = \cot(\pi - c)$

$\frac{ cota \: cotb \: - 1}{ cotb + cota } = - \cot(c)$

$\cot(a) \cot(b) - 1 = - \cot(b) \cot(c) - \cot(c) \cot(a)$

$\cot a . cotb + cotb. cotc + cotc. cota = 1$