Question

in any trangle ABC prove that B-C/2=B+C sinA/2

Answer 1

Answer:

Let a/sin A = b/sin B = c/sinC = k

Then,

a = k sinA, b = k sinB, c = k sinC

RHS

b-c/a cos A/2

= (ksinB - ksinC/k sinA )cos A/2

= {[2 cos B+C/2 Sin B-C/2]/ Sin A} cos A/2

=[2* Sin B-C/2 cos (pi/2-A/2) .cos A/2] / sinA

= [SinA* sinB-C/2] / sinA

= Sin B-C/2

= LHS

Hence proved

Step-by-step explanation: