Home
Class 11
MATHS
In any DeltaABC, prove that asin(B-C)+...

In any `DeltaABC`, prove that
`asin(B-C)+bsin(C-A)+csin(A-B)=0`

Text Solution

Verified by Experts

1st term =`asin(B-C)`
`=ksinA.sin(B-C)`
`=ksin{180^(@)-(B+C)}sin(B-C)`
`ksin(B+C).sin(B-C)`
`=ksin^(2)B-sin^(2)C`
Similarly,
2nd term `=k(sin^(2)C-sin^(2)A)`
3rd term `=k(sin^(2)A-sin^(2)B)`
Now L.H.S. `=asin(B-C)+bsin(C-a)+csin(A-B)`
`=k(sin^(2)B-sin^(2)C)+k(sin^(2)C-sin^(2)A)+k(sin^(2)A-sin^(2)B)`
`ksin^(2)B-ksin^(2)C-ksin^(2)A+ksin^(2)A-ksin^(2)B` =0 = RHS Hence Proved.
Promotional Banner

Topper's Solved these Questions

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise EXERCISES 3A|12 Videos

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise EXERCISES 3B|24 Videos

  • STRAIGHT LINES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise|207 Videos

Similar Questions

Explore conceptually related problems

In any triangle A B C , prove that: \ asin(B-C)+b sin(C-A)+csin(A-B)=0

In any DeltaABC , prove that a(sinB-sinC)+b(sinC-sinA)+c(sinA-sinB)=0

In any DeltaABC prove that, a^(3)sin(B-C)+b^(3)sin(C-A)+c^(3)sin(A-B)=0 .

In a DeltaABC , prove that : sin3A sin(B-C)+sin3B sin(C-A) + sin3C sin (A-B)=0 .

In any triangle A B C , prove that: \ a^3sin(B-C)+b^3sin(C-A)+c^3sin(A-B)=0

In any DeltaABC , prove that asin(A/2+B)=(b+c)sin""A/2

In any DeltaABC , prove that asin""1/2(B-C)=(b-c)cos""1/2A

In any DeltaABC , prove that (sinA)/(sin(A+B))=a/c

In any DeltaABC , prove that (sin B)/(sin(B+C) ) = b/a

In DeltaABC , prove that: bsinB-c sinC=asin(B-C)