Maharashtra State BoardHSC Arts 12th Board Exam
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In ∆ABC, if sin2A + sin2B = sin2C, then show that a2 + b2 = c2 - Mathematics and Statistics

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Sum

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

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Solution

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 

Concept: Solutions of Triangle
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