Home
Class 12
MATHS
In a DeltaABC, Sin A /SinC = sin(A-B)/ s...

In a `DeltaABC`, `Sin A /SinC = sin(A-B)/ sin(B - C)` , then `a^2, b^2, c^2` are in

A

AP

B

GP

C

HP

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`because(sinA)/(sinC)=(sin(A-B))/(sin(b-C))`
`rArr(sinA)/(sinC)=(sinAcosB-cosAsinB)/(sinBcosC-cosBsinC)`
`rArr(a)/(c)=(acosB-bcosA)/(bcosC-c cosB)`
`rArrabcosC+bccc cosA=2ac cosB`
`rArr(a^(2)+b^(2)-c^(2))/(2)+(b^(2)+c^(2)-a^(2))/(2)=2(c^(2)+a^(2)-b^(2))/(2)`
`rArra^(2)+c^(2)=2ab^(2)`
Hence , `a^(2)+b^(2)andc^(2)` are AP.
Promotional Banner

Similar Questions

Explore conceptually related problems

If in a DeltaABC, sin A: sin C = sin (A - B): sin (B-C), then a^(2), b^(2), c^(2) are in

In a Delta ABC,(sin A)/(sin C)=(sin(A-B))/(sin(B-C)), then a^(2),b^(2),c^(2) are in

In DeltaABC if (sinA)/(sinC)=(sin(A-B))/(sin(B-C)) , then a^(2), b^(2), c^(2) are in :

In DeltaABC , (sinA)(sinC) = (sin(A-B))/(sin(B-C)) , prove that a^(2),b^(2),c^(2) are in A.P.

If (sin A)/(sin C)=(sin(A-B))/(sin(B-C)), prove that a^(2),b^(2),c^(2) are in A.P.

If in a /_ABC,(sin A)/(sin C)=(sin(A-B))/(sin(B-C)) then a^(2):b^(2):c^(2)

In any DeltaABC , sin A + sin B + sin C =

In a DeltaABC,R^(2) (sin 2A+sin 2B+sin 2C)=

In a triangle ABC, if sin A sin(B-C)=sinC sin(A-B) , then prove that cos 2A,cos2B and cos 2C are in AP.