sin^2 A/2+sin^2 B/2-sin^2 C/2=1-2cosA/2cosB/2sinC/2
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Answer:
4Rsin(A/2)cos(B/2)cos(C/2)
=4R
bc
(s−b)(s−c)
ac
s(s−b)
ab
s(s−c)
=
abc
4R
s
2
(s−b)
2
(s−c)
2
=
abc
4R
S(s−b)(s−c)
=
S
1
×
(s−a)
S
2
=
s−a
S
=r
1
(ii) 4RcosA/2sinB/2cosC/2
=4R
bc
s(s−a)
ac
(s−a)(s−c)
ab
s(s−c)
=
abc
4R
s
2
(s−a)
2
(s−c)
2
=
S
1
(s−b)
S
2
=
s−b
S
=r
2
(iii) 4RcosA/2cosB/2sinC/2
=4R
bc
s(s−a)
ac
s(s−b)
ab
(s−a)(s−b)
⇒
abc
4R
s
2
(s−a)
2
(s−b)
2
S
1
s−c
S
2
=
s−c
S
=r
3
proved.
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