If in a , the altitudes from the vertices on opposite sides are in H.P, then are in :

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JEE Main 2018 Properties of Triangle: If in a , the altitudes from the vertices on opposite sides are in H.P, then are in :...

The correct answer is A. are in are in are in are in are in are in

If in a , the altitudes from the vertices on opposite sides... | JEE Main 2018 Properties of Triangle

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Question

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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Solution

$\Delta = {1 \over 2}{p_1}a = {1 \over 2}{p_2}b = {1 \over 2}{p_3}b$ ${p_1},{p_2},{p_3},$ are in $H.P.$ $\Rightarrow {{2\Delta } \over a},{{2\Delta } \over b},{{2\Delta } \over c}$ are in $H.P.$ $\Rightarrow {1 \over a},{1 \over b},{1 \over c},$ are in $H.P.$ $\Rightarrow a,b,c$ are in $A.P.$ $\Rightarrow$ $K\sin A,K\sin B,K\sin C$ are in $A.P.$ $\Rightarrow$ $\sin A,\sin B,\sin C$ are in $A.P.$

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