Home
Class 11
MATHS
For any triangle ABC, prove that(b+c)cos...

For any triangle ABC, prove that`(b+c)cos((B+C)/2)=acos((B-C)/2)`

Text Solution

Verified by Experts

We know, `a/sinA = b/sinB = c/sinC = k`
where, k is a constant.
`:. (b+c)/a = (k(sinB+sinC))/(ksinA)`
`= (sinB+sinC)/sinA`
`=(2sin((B+C)/2)cos((B-C)/2))/(2sinA/2cosA/2)`
As, `A+B+C = 180, So, B+C = 180-A`
`:. (b+c)/a=(sin((180-A)/2)cos((B-C)/2))/(sin((180-(B+C))/2)cosA/2)`
...
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    NCERT|Exercise SOLVED EXAMPLES|33 Videos

  • TRIGONOMETRIC FUNCTIONS

    NCERT|Exercise EXERCISE 3.4|9 Videos

  • TRIGONOMETRIC FUNCTIONS

    NCERT|Exercise EXERCISE 3.1|7 Videos

  • STRAIGHT LINES

    NCERT|Exercise EXERCISE 10.5|2 Videos

Similar Questions

Explore conceptually related problems

In any Delta ABC, prove that :(b+c)cos((B+C)/(2))=a cos((B-C)/(2))])

In DeltaABC , prove that: (b+c)cos(B+C)/(2)=acos(B-C)/(2)

In any triangle ABC, prove that: (b-c)cot(A)/(2)+(c-a)cot(B)/(2)+(a-b)cot(C)/(2)=0

For any triangle ABC, prove that (cos A)/(a)+(cos B)/(b)+(cos C)/(c)=(a^(2)+b^(2)+c^(2))/(2abc)

In any DeltaABC , prove that ((b+c))/acos""((B+C))/2=cos""((B-C))/2

In any triangle ABC, prove that: a cos((B+C)/(2))=(b+c)(sin A)/(2)

For any triangle ABC,prove that a(b cos C-c cos B)=b^(2)-c^(2)

For any triangle ABC ,prove that (a+b)/(c)=(cos((A-B)/(2)))/(sin(C)/(2))

For any triangle ABC ,prove that (a-b)/(c)=(sin((A-B)/(2)))/(cos(C)/(2))

For any triangle ABC, prove that (sin(B-C))/(2)=(b-c)/(a)((cos A)/(2))])