Question

Sin(a-b)/sin(a+b)=a2-b2/c2

Answer 1

Answer:

Step-by-step explanation:

By Sine rule we have,

a/SinA = b/SinB = c/SinC = k.

=> a = kSinA, b = kSinB, c = kSinC

Now,

a² - b² / c²

=> k²Sin²A - k²Sin²B / k²Sin²C

=> Sin²A - Sin²B / Sin²C

//we know that Sin²A - Sin²B = Sin(A+B)Sin(A-B)

A+B+C = π => C = π - (A+B) => SinC = Sin(π - (A+B))

=> Sin(A+B)Sin(A-B) / Sin²[π -(A+B)]

=> Sin(A+B)Sin(A-B) / Sin²(A+B)

=> Sin(A - B)/Sin(A+B)

Hence Proved.