question_answer

If in a\[\Delta ABC,\]the altitudes from the vertices A,B,C on opposite sides are in HP, then sin A, sin B, sin C are in     AIEEE  Solved  Paper-2005

A) HP

B) Arithmetico-Geometric Progression

C) AP

D) GP

Correct Answer: C

Solution :

Since, in            Similarly, and Since, AD,CE,CF are in HP.  arein HP.  are in AP.  are in AP. Alternate Solution area     Similarly, and AD, BE, CF are in HP. are in HP. a, b, c are in AP. \[\Rightarrow \,\sin A,\,\sin B,\,\sin C\] are in AP.