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In AABC, prove thatcot_ + cot _ + cotー-cot-cot-cot-.BC222 |
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Answer» If ABC is a triangleA + B + C = π=> A/2 + B/2 = π/2 - C/2=> tan (A/2 + B/2) = tan (π/2 - C/2)=> (tan A/2 + tanB/2) / (1 - tan A/2 tan B/2) = cot C/2=> (cot A/2 + cot B/2) / (cot A/2 cot B/2 - 1) = cot C/2=> cot A/2 + cot B/2 + cot C/2 = cot A/2 cot B/2 cot C/2Of course its only true when ABC are angles of a triangle |
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