In a ΔABC, if (sinA+sinB+sinC) (sinA+sinB−sinC) = 3sinAsinB, then the angle C is equal to [AMU 1999]

π2

π3

π4

π6

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In a ΔABC, if (sinA+sinB+sinC) (sinA+sinB−sinC) = 3sinAsinB, then the angle C is equal to [AMU 1999]

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Text solutionVerified

(a+b+c)(a+b−c)=3ab Þ a2+b2−c22ab=12⇒cosC=cosπ3⇒∠C=π/3

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Question Text	In a ΔABC, if (sinA+sinB+sinC) (sinA+sinB−sinC) = 3sinAsinB, then the angle C is equal to [AMU 1999]
Answer Type	Text solution:1
Upvotes	150