Question

Prove that:
Δ=4.R.r.cos a/2.cos b/2. cos y/2

Answer 1

\[\frac{ abc }{ 4\Delta } * \frac{ \Delta }{ S } * \sqrt{\frac{ s(s-a) }{ bc }} * \sqrt{\frac{ s(s-b) }{ ac }} * \sqrt{\frac{ s(s-c) }{ ab }}\]

Answer 2

Using R.H.S

Answer 3

it is easy just do the multiplication.
let the triangle sign be t
so rhs=
4[abc/4t][t/s][sqrt(s(s-a)/bc)][sqrt(s(s-b)/ac)][sqrt(s(s-c)/ab)]
=[4abct/4ts][(s/abc)sqrt(s(s-a)(s-b)(s-c))]
=[abc/s][s/abc]sqrt(s(s-a)(s-b)(s-c))
=sqrt(s(s-a)(s-b)(s-c))
=t
hence proved