(1) Consider a right angle triangle ABC, right angle at A and B=C=45° Then, b=c is also true. Hence, for the given condition, ΔABC must not be an obtuse-angled triangle.
InΔABC,∠A=40°,∠B=65° ∠C=180°−40°−65°=75° From sine rule,
a
sin40°
=
c
sin75°
∴
a
c
=sin40°.cosec75° So,
a
c
≠sin40°.cosec15° Hence, ΔABC is not possible. Thus, statement (2) is correct.