If in a Delta ABC,the altitudes from the vert | vedclass

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(D) Let the altitudes from vertices $A, B, C$ be $h_a, h_b, h_c$ respectively.We know that $h_a = \frac{2\Delta}{a}$,$h_b = \frac{2\Delta}{b}$,and $h_

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$A.P.$

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(D) Let the altitudes from vertices $A, B, C$ be $h_a, h_b, h_c$ respectively.We know that $h_a = \frac{2\Delta}{a}$,$h_b = \frac{2\Delta}{b}$,and $h_c = \frac{2\Delta}{c}$,where $\Delta$ is the area of the triangle.Given that $h_a, h_b, h_c$ are in $H.P.$,we have $\frac{2\Delta}{a}, \frac{2\Delta}{b}, \frac{2\Delta}{c}$ are in $H.P.$This implies that $\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in $H.P.$Therefore,$a, b, c$ are in $A.P.$By the Sine Rule,$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2R$.Thus,$a = 2R \sin A$,$b = 2R \sin B$,and $c = 2R \sin C$.Since $a, b, c$ are in $A.P.$,it follows that $2R \sin A, 2R \sin B, 2R \sin C$ are in $A.P.$Hence,$\sin A, \sin B, \sin C$ are in $A.P.$

If in a $\Delta ABC$,the altitudes from the vertices $A, B, C$ on opposite sides are in $H.P.$,then $\sin A, \sin B, \sin C$ are in

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