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In DeltaABC, prove that: <br> ...

# In DeltaABC, prove that: <br> (a+b+c)(tanA/2+tanC/2)=2bcotB/2

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Solution :
LHS =(a+b+c)(tanA/2+tanC/2) <br> =2s. sqrt((s-b)(s-c))/(s(s-a)) + sqrt((s-a)(s-b))/(s(s-c)) <br> =2s.sqrt((s-b)/(s))[(s-c)/(s-a)+sqrt((s-a)/(s-c))] <br> =2sqrt(s(s-b))[(s-c+s-a)/(sqrt((s-a)(s-c)))(2s-a-c)] <br> 2cotB.2.(a+b+c-a-c) <br> =2bcotB/2=RHS

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