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1998

JEE Main 1998 Mathematics question on Trigonometry

If in a △PQR\triangle PQR, sin⁡P\sin P, sin⁡Q\sin Q, sin⁡R\sin R are in AP, then
  1. A.
    the altitudes are in AP
  2. B.
    the altitudes are in HP
  3. C.
    the medians are in GP
  4. D.
    the medians are in AP
Show answer and solution

Correct option: B

Solution

Sin P, sin Q, sin R in AP means by the sine rule, sides p, q, r are in AP.

The altitudes are hp = 2Δ/p, hq = 2Δ/q, hr = 2Δ/r. Since p, q, r are in AP, their reciprocals 1/p, 1/q, 1/r are in HP, so hp, hq, hr are in HP.

[1998]

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