Home
Class 11
MATHS
Prove that in triangleABC, a^3cos(B-C)+b...

Prove that in `triangleABC, a^3cos(B-C)+b^3cos(C-A)+c^3cos(A-B)=3abc`

Text Solution

Verified by Experts

From sine law, we have,
`a/sinA = b/sinB = c/sinC = k`
`=> a = ksinA, b = ksin B, c = ksinC`
Now,
`L.H.S. = a^3cos(B-C)+b^3cos(C-A)+c^3cos(A-B)`
`=a^2(ksinAcos(B-C))+b^2(ksinBcos(C-A))+c^2(ksinCcos(A-B))`
`=a^2(ksin(pi-(B+C))cos(B-C))+b^2(ksin(pi-(C+A))cos(C-A))+c^2(ksin(pi-(A+B))cos(A-B))`
`=k/2[a^2(2sin(B+C)cos(B-C))+b^2(2sin(C+A)sin(C-A))+c^2(2sin(A+B)cos(A-B))]`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

In any triangle ABC, prove that, a^(3) cos(B-C) + b^(3) cos(C-A) + c^(3) cos(A-B) = 3abc.

In Delta ABC prove that a^3cos(B-C) + b^3cos(C-A) + c^3 cos(A-B) = 3abc

In /_\ABC show that a^3cos(B-C)+b^3cos(C-A)+c^3cos(A-B)=3abc

In a DeltaABC prove that: a^3cos(B-C)+b^3cos(C-A)+c^3cos(A-B)=3abc

Prove that a^(3) cos (B-C) + b^(3) cos (C - A) + c^(3) cos (A-B) = 3abc .

In any triangle A B C , prove that: a^3cos(B-C)+b^3cos(C-A)+c^3cos(A-B)=3a b c

In Delta ABC, prove that a^(3)cos(B-C)+b^(3)cos(C-A)+c^(3)cos(A-B)=3abc

In any triangle ABC, prove that: a^(3)cos(B-C)+b^(3)cos(C-A)+c^(3)cos(A-B)=3abc