Question

SinA/sinC=sin(A-B)/sin(B-C), prove that a2, b2, c2 are in A. P

Answer 1

In a triangle, A+B+C=180

sin A/sinC=sin(180-(B+C))/sin(180-(A+B))

sin(B+C)/sin(A+B) =sin(A-B)/sin(B-C)

sin²B-sin²C=sin²A-sin²B

2sin²B=sin²A+sin²C

we know that a=2RsinA,b=2RsinB,c=2RsinC


2(b/2R)²=(a/2R)²+(c/2R)²

2b²=a²+c²


so a²,b²,c² are in A.p .....


I hope this will help u;)