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JEE MainMathematicsModerate

If in a △ABC, the altitudes from the vertices A,B,C on opposite
sides are in H.P., then sinA, sinB, sinC are in

Show answer and solution
2Δ2,2Δb,2Δc\frac{2\Delta}{2},\frac{2\Delta}{b},\frac{2\Delta}{c} → H.P.
⇒a2Δ,b2Δ,c2Δ\Rightarrow \frac{a}{2\Delta},\frac{b}{2\Delta},\frac{c}{2\Delta} →
A.P.
⇒\Rightarrow a, b, c → A.P.
⇒\Rightarrow sinA, sinB, sinC → A.P.

Source: Grass-G / M-24 Mathematics Paper 31 Dec.docx

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