Question

a sin(A/2+B)=(b+c)sinA/2​

Answer 1

Answer:

Let AD - bissector of A.

BD/CD=c/b

BD+CD=a

(a-CD)/CD=c/b => CD=ab/(b+c)

Triangle ABD: Angle ADC=A/2 + B

SIN-theorem : sin DAC/CD = sin ADC/b

i.e. (sin A/2)/(ab/(b+c)) = sin (A/2+B)/b

sin A/2 (b+c)=a sin (A/2+B)

So it goes.

Answer 2

Answer:

सत्यमेव जयते नानृतम सत्येन पंथा विततो देवयानः। येनाक्रमंत्यृषयो ह्याप्तकामो यत्र तत् सत्यस्य परमम् निधानम॥