For any triangle ABC, prove that b+c/a=cos(B-C/2)/sin (A/2)
abc , 5 Years ago
Grade 11
Trigonometry> For any triangle ABC, prove that b+c/a=co...
1 AnswersVikas TU
Last Activity: 5 Years ago
Dear student
RHS
(b+C)SinA/2 = (kSinB +KSinC )SinA/2 = k(SinB+SinC)SinA/2
k+2Sin(B+C)/2 *Cos(B-C)/2 *Sin(A/2) = 2k Sin(pie/2 -A/2)Cos(B-C)/2 SinA/2
=> 2KCosA/2 Cos(B-C)/2 SinA/2 = k (2SinA/2CosA/2) Cos(B-C)/2
KsinA =a =LHS
(b+C)SinA/2 = (kSinB +KSinC )SinA/2 = k(SinB+SinC)SinA/2
k+2Sin(B+C)/2 *Cos(B-C)/2 *Sin(A/2) = 2k Sin(pie/2 -A/2)Cos(B-C)/2 SinA/2
=> 2KCosA/2 Cos(B-C)/2 SinA/2 = k (2SinA/2CosA/2) Cos(B-C)/2
KsinA =a =LHS
LHS = RHS
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