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Question

In ΔABC,let L,M,N be the feet of the altitudes. Then calculate sin(MLN)+sin(LMN)+sin(MNL)

A
4sinAsinBsinC
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B
3sinAsinBsinC
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C
2sinAsinBsinC
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D
sinAsinBsinC
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Solution

The correct option is A 4sinAsinBsinC
Using properties of pedal triangle,
we have MLN=1802A
LMN=1802B
MLN=1802C
sin(MLN)+sin(LMN)+sin(MNL)=sin2A+sin2B+sin2C =4sinAsinBsinC

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