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if a,b,c are in A.P. then Tan A/2, Tan B/2, Tan C/2 are in ?

if a,b,c are in A.P. then Tan A/2, Tan B/2, Tan C/2 are in ?

Grade:9

1 Answers

Akshay
185 Points
5 years ago
If a,b,c are in AP. Then, (s-a),(s-b),(s-c) are also in AP.
tan(A/2) = rt[ (s-b)*(s-c) / s(s-a) ] = rt[ (s-a)*(s-b)*(s-c) / s ] / (s-a)..........{by multiplying and dividing by (s-a)}
//ly tan(B/2) = rt[ (s-a)*(s-b)*(s-c) / s ] / (s-b)
and tan(C/2) = rt[ (s-a)*(s-b)*(s-c) / s ] / (s-c)
So, tan(A/2),tan(B/2) and tan(C/2) are in HP.

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