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Q.

If sin2A2sin2B2sin2C2  are in H.P., then show that a,b,c are in H.P. 

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Detailed Solution

 sin2A2,sin2B2,sin2C2 are in H.P. 

bc(sb)(sc),ca(sc)(sa),ab(sa)(sb)  are  in H.P. 

2ca(sc)(sa)=bc(sb)(sc)+ab(sa)(sb)

2ca(sc)(sa)=bc(sa)+ab(sc)(sa)(sb)(sc)

2ca(sb)=bc(sa)+ab(sc)

2cas2abc=bcsabc+absabc

2cas=sb(c+a)

b=2aca+c     a,b,c  are in H.P.

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