Sat June 09, 2012 By:

*In any triangleABC,prove that(c^2+b^2-a^2)tanA=(a^2+c^2-b^2)tanB=(a^2+b^2-c^2)tanC *In any triangleABC, If angleC=60degree prove that 1/a+c + 1/b+c = 1/a+b+c

Expert Reply
Tue June 12, 2012
We would request you to please ask one question at a time. The answer to your first question is as follows:
We need to prove that (c2+b2-a2)tanA=(a2+c2-b2)tanB=(a2+b2-c2)tanC
i.e., we need to prove (c2+b2-a2)sinA/ cosA = (a2+c2-b2)sinB/cosB = (a2+b2-c2)sinC/cosC
i.e., we need to prove 2bc sinA = 2ac sinB = 2ab sinC
[Using cosine formula]
Now divide by 2abc,
We need to prove sinA/a = sinB/b = sinC/c
which is true by sine formula
Hence, the given statement is true.
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