For any triangle ABC, prove the following identity: tanA + tanB + tanC = tanA ta

ID: 3090563 • Letter: F

Question

For any triangle ABC, prove the following identity:
tanA + tanB + tanC = tanA tanB tanC
hints: all the angles in a triangle add up to 180 think about the relationship between the tangents of two anglesthat are supplementary

Thanks for any help! For any triangle ABC, prove the following identity:
tanA + tanB + tanC = tanA tanB tanC
hints: all the angles in a triangle add up to 180 think about the relationship between the tangents of two anglesthat are supplementary

Thanks for any help!
tanA + tanB + tanC = tanA tanB tanC
hints: all the angles in a triangle add up to 180 think about the relationship between the tangents of two anglesthat are supplementary

Thanks for any help!

Explanation / Answer

tan A + tan B + tan C = tan A + tan B + tan (180 - (A+B)) tan A + tan B + tan C = tan A + tan B - tan (A+B) tan A + tan B + tan C = tan A + tan B - (tan A + tanB)/(1-tan A tan B) tan A + tan B + tan C = [tan A(1-tan A tan B) + tan B(1-tan Atan B)]/(1-tan A tan B)- (tan A + tanB)/(1-tan A tan B) tan A + tan B + tan C = [tan A -tan^2 A tan B + tan B - tan Atan^2 B - tan A - tan B]/(1-tan A tan B) tan A + tan B + tan C = (-tan^2 A tan B - tan A tan^2B)/(1-tan A tan B) tan A + tan B + tan C = (tan^2 A tan B + tan A tan^2B)/(tan A tan B - 1) tan A + tan B + tan C = tan A tan B [(tan A + tanB)/(tan A tan B - 1)] tan A + tan B + tan C = tan A tan B [ -(tan A + tanB)/(1 - tan A tan B)] tan A + tan B + tan C = tan A tan B tan [180 - (A + B)] tan A + tan B + tan C = tan A tan B tan C

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For any triangle ABC, prove the following identity: tanA + tanB + tanC = tanA ta

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Explanation / Answer

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