Home
Class 11
MATHS
In DeltaABC, prove that: a(bcosC-(c)co...

In `DeltaABC`, prove that:
`a(bcosC-(c)cosB)=b^(2)-c^(2)`

Text Solution

Verified by Experts

LHS. `=a(bcosC-(c)cosB)`
`=abcosC-a(c)cosB`
`=ab.(a^(2)+b^(2)-c^(2))/(2ab)-ac.(c^(2)+a^(2)-b^(2))/(2ca)`
`=(a^(2)+b^(2)-c^(2))/(2)-(c^(2)+a^(2)-b^(2))/(2)`
`=(a^(2)+b^(2)-c^(2)-c^(2)+a^(2)-b^(2))/(2)`
`=2(b^(2)-c^(2))/(2)`
`=b^(2)-c^(2)`= RHS Hence Proved.
Promotional Banner

Topper's Solved these Questions

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise EXERCISES 3A|11 Videos

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise EXERCISES 3B|22 Videos

  • STRAIGHT LINES

    NAGEEN PRAKASHAN|Exercise Exercise|206 Videos

Similar Questions

Explore conceptually related problems

In any DeltaABC , prove that a(bcosC-c cosB)=(b^(2)-c^(2))

In DeltaABC , prove that: a(cosC-cosB)=2(b-c)cos^(2)A/2

In DeltaABC , prove that: acosA+bcosB=(c)cos(A-B)

In DeltaABC , prove that: c(acosB-b cosA)=a^(2)-b^(2)

With usual notatons , in triangle ABC , prove that a(bcosC-c cos B)=b^2-c^2 .

In any DeltaABC , prove that ac cosB-bc cosA=(a^(2)-b^(2))

In DeltaABC , prove that: (bcos^(2)C)/2+(c cos^(2)B)/2=s

In DeltaABC , prove that: b(cosA-cosC)=2(c-a)cos^(2)B/2

In DeltaABC , prove that: a(cosB+cosC)=2(b+c)sin^(2)A/2 .

In DeltaABC , prove that cos^(2)A/2+cos^(2)B/2-cos^(2)C/2=2cosA/2cosB/2sinC/2