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tanA+tanB+tanC=tanA.tanB.tanc if nπ=A+B+CIs this is valid in right angled triangle if one of the angle is 90°?? for eg=Angle A=90°

tanA+tanB+tanC=tanA.tanB.tanc if nπ=A+B+CIs this is valid in right angled triangle if one of the angle is 90°?? for eg=Angle A=90°

Grade:11

1 Answers

Vikas TU
14149 Points
3 years ago
Dear Student,
A+B+C=n pi (given)
=>A+B=n pi-C
=>tan(A+B)=tan(n pi-C)
if we apply tan(A+B) formula:
(tan A+tan B)/(1-tan A.tanB) = tan(n pi-C)
but tan(n pi-C)=-tan C
so tanA+tanB=-tanC(1-tanA.tanB)
tan A+tanB=tanA.tanB.tanC -tan C
=> tan A+tanB+tanC=tan A.tanB.tan C
As we have not assumed any particular type of triangle, the above proof is applicable for all triangles including right angled triangle.
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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