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Question

In ΔABC, if sin2A2,sin2B2,sin2C2 are in H.P., then a,b,c are in

A
H.P.
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B
A.P.
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C
G.P.
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D
None of the above
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Solution

The correct option is A H.P.
sin2A2, sin2B2, sin2C2 are in H.P.
1sin2A2, 1sin2B2, 1sin2C2 are in A.P.
1sin2C21sin2B2=1sin2B21sin2A2
ab(sa)(sb)ac(sa)(sc)=ac(sa)(sc)bc(sb)(sc)
asa(b(sc)c(sb)(sb)(sc))=csc(a(sb)b(sa)(sa)(sb))
abac=acbc
ab+bc=2ac1c+1a=2b
Hence, a,b,c are in H.P.

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