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Question
Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`
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Solution
cot(A + B) = `1/(tan("A" + "B"))`
= `1/((tan "A" + tan "B")/(1 - tan "A" tan "B"))`
= `(1 - tan"A" tan"B")/(tan"A" + tan "B")`
= `(1 - 1/cot"A" * 1/cot"B")/(1/cot "A" + 1/cot"B")`
= `((cot"A" cot"B" - 1)/(cot"A" cot"B"))/((cot"B" + cot"A")/(cot"A" cot"B"))`
cot(A + B) = `(cot"A" cot"B" - 1)/(cot"A" + cot"B")`
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