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IF A+B+C=180,prove that (cos A/(sinB sinC)) +( cosB/(sinC sinA)) + (cosC/(sinA sin B))=2

IF A+B+C=180,prove that (cos A/(sinB sinC)) +( cosB/(sinC sinA)) + (cosC/(sinA sin B))=2

Grade:12th pass

1 Answers

Arun
25757 Points
4 years ago
Dear student
 
sin A cosA + sinB cosB + sinc cos C / sinA sinB sinC
 
sin 2A + sin 2B + sin2C / 2 sinA sinB sinC
 
but for a triangle
 
SIn 2A + sin 2B + sin2C = 4 sinA sinB sinC
 
hence its answer will be = 4/2 = 2

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