JEE Advance - Mathematics (1994 - No. 38)
Consider the following statements connecting a triangle $$ABC$$
(i) The sides $$a, b, c$$ and area $$\Delta $$ are rational.
(ii) $$a,\tan {B \over 2},\tan {c \over 2}$$ are rational.
(iii) $$a,\sin A,\sin B,\sin C$$ are rational.
Prove that $$\left( i \right) \Rightarrow \left( {ii} \right) \Rightarrow \left( {iii} \right) \Rightarrow \left( i \right)$$
Statement (i) implies statement (ii)
Statement (ii) implies statement (iii)
Statement (iii) implies statement (i)
All three statements are equivalent
None of the above implications hold