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In ΔΑ1C, prove that(i)tan A + tan B .i tan Ctan A tan B tan CA B C2cot--+ cot,i. cot |
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Answer» We have to prove that tan A + tan B + tan C = tan A*tan B*tan C for any non-right angle triangle.For any triangle the sum of the angles is equal to 180 degrees. If we take a triangle ABC, A + B + C = 180 degrees. A + B + C = 180 or A + B = 180 - Ctan (A + B) = tan (180 - C) = tan C=> (tan A + tan B)/(1 - tan A*tan B) = tan C=> tan A + tan B = tan C - tan A*tan B*tan C=> tan A + tan B + tan C = tan A*tan B*tan CThis proves that tan A + tan B + tan C = tan A*tan B*tan C next part |
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