In triangle ABC, prove that b=acosC + ccosA and use this result to prove that 2[asin2C/2 + csin2A/2] = a+c - Maths - Trigonometric Functions

Question

In triangle ABC, prove that b=acosC + ccosA and use this result
to prove that 2[asin2C/2 + csin2A/2] = a+c -
b

Priyanka Kedia · Accepted Answer

R H S
=a cosC+c cosA          =aa2+b2-c22ab+cb2+c2-a22bc          =a2+b2-c22b+b2+c2-a22b          =12ba2+b2-c2+b2+c2-a2          =12b2b2          =b          =L
H S Hence ProvedNow,L H S
=2asin2C2+csin2A2          =2a1-cosC2+c1-cosA2          =a-a cosC+c-c cosA          =a+c-a cos C+c cosA          =a+c-b          =R
H S Hence Proved

In triangle ABC, prove that b=acosC + ccosA and use this result to prove that 2[asin2C/2 + csin2A/2] = a+c - b

In triangle ABC, prove that b=acosC + ccosA and use this result to prove that 2[asin²C/2 + csin²A/2] = a+c - b