Question

In ∆ABC, if sin²A + sin²B = sin²C, then show that a² + b² = c² 

Answer 1

In ∆ABC by sine rule, we have

`(sin"A")/"a" = (sin"B")/"b" = (sin"C")/"c"` = k

∴ sin A = ka, sin B = kb, sin C = kc

Now, sin²A + sin²B = sin²C    .......[Given]

∴ k²a² + k²b² = k²c²

∴ a² + b² = c²