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if A+B+C=pi ad sin(A+ B/2)=k sin C/2 then tanA/2 tanB/2

if A+B+C=pi ad sin(A+ B/2)=k sin C/2 then tanA/2 tanB/2

Grade:11

1 Answers

Vijay Mukati
askIITians Faculty 2590 Points
4 years ago
Dear Student,

I think your questions should be
if A+B+C=pi ad sin(A+ C/2)=k sin C/2 then tanA/2 tanB/2

Solution:

sin(A+C/2)=sin{A+(π/2-A/2-B/2)
=sin(π/2+A/2-B/2)=cos(A/2-B/2)
sinC/2=sin(π/2-A/2-B/2)=cos(A/2+B/2)
Since, sin(A+C/2)=ksinC/2,
so cos(A/2-B/2)= kcos(A/2+B/2)
cosA/2cosB/2+sinA/2sinB/2=kcosA/2cosB/2-ksinA/2sinB/2
1+tanA/2tanB/2=k-ktanA/2tanB/2
tanA/2tanB/2=(k-1)/(k+1).

Thanks Vijay

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