Home
Class 10
MATHS
If A, B and C are interior angles of a t...

If A, B and C are interior angles of a triangle ABC, then show that `"sin"((B+C)/2)=cos(A/2)` .

Text Solution

Verified by Experts

`R.H.S. = cos(A/2)`
As we know, `A+B+C = 180^@`
`A = 180-(B+C)`
`:.cosA/2 = cos((180-(B+C))/2)=cos(90-(B+C)/2)` As we know, `cos(90-x) = sinx`
`:.cosA/2 = sin((B+C)/2)=L.H.S.`
Promotional Banner

Similar Questions

Explore conceptually related problems

If A, B and C are interior angles of a triangle ABC, then show that "sin"((B+C)/2)=cosA/2 .

if A, B and C are interior angles of a triangle ABC, then show that cos((B+C)/2) = sin (A/2)

if A, B and C are interior angles of a triangle ABC, then show that cos((B+C)/2) = sin (A/2)

If A, B and C are interior angles of a DeltaABC , then show that cot((B+C)/(2))=tan((A)/(2)) .

For triangle ABC, show that "sin"(A+B)/2="cos"C/2

If A ,\ B ,\ C are the interior angles of a triangle A B C , prove that tan(B+C)/2=cotA/2

For triangle ABC, show that: sin((A+B)/(2))-cos(C)/(2)=0

If A ,\ B ,\ C are the interior angles of a triangle A B C , prove that tan((C+A)/2)=cotB/2 (ii) sin((B+C)/2)=cosA/2

For triangle ABC, show that "tan"(B+C)/2="cot"A/2

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