Properties of triangles

If a,b,c are in H.P..
prove that :
sin²A2,sin²B2 and sin²C2 ARE ALSO IN h.p.

2 Answers

1357

Manish Shankar ·2014-01-30 04:45:10

1/a, 1/b, 1/c are in AP

=>s/a, s/b, s/c are in AP

=>s/a - 1, s/b - 1, s/c - 1 are in AP

=>(s-a)/a, (s-b)/b, (s-c)/c are in AP

=>(s-a)/aÎ”², (s-b)/bÎ”², (s-c)/cÎ”² are in AP

=>(s-a)/(as(s-a)(s-b)(s-c)), (s-b)/(bs(s-a)(s-b)(s-c)), (s-c)/(cs(s-a)(s-b)(s-c)) are in AP

=>1/(a(s-b)(s-c)), 1/(b(s-a)(s-c)), 1/(c(s-a)(s-b)) are in AP

=>bc/((s-b)(s-c)), ac/((s-a)(s-c)), ab/((s-a)(s-b)) are in AP

=>1/sin²(A/2), 1/sin²(B/2), 1/sin²(C/2) are in AP

466

Himanshu Giria ·2014-01-29 08:40:05

somebody plz try this one out ... ..

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