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In DeltaABC if sin^2(A/2), sin^2(B/2), s...

In `DeltaABC` if `sin^2(A/2), sin^2(B/2), sin^2(C/2)` are in H.P then `a,b,c` will be in

A

AP

B

GP

C

HP

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Here , `(1)/("sin"^(2)(A)/(2)),(1)/("sin"^(2)(B)/(2))and(1)/("sin"^(2)(C)/(2))` are in AP .
`rArr(1)/("sin"^(2)(C)/(2))-(1)/("sin"^(2)(B)/(2))=(1)/("sin"^(2)(B)/(2))-(1)/("sin"^(2)(A)/(2))`
`rArr(ab)/((s-a)(s-b))-(ac)/((s-a)(s-c))=(ac)/((s-a)(s-c))-(bc)/((s-b)(s-c))`
`rArr((a)/(s-a))[(b(s-c)-c(s-b))/((s-b)(s-c))]=((c)/(s-c))[(a(s-b)-b(s-a))/((s-a)(s-b))]`
`rArra(bs-cs)=c(as-bs)`
`rArrab+bc=2acrArr(1)/(c)+(1)/(a)=(2)/(b)`
Hence , a , b and , c are in HP.
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