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Find cot(a/2) + cot(b/2) + cot(c/2), if a + b + c = 180.

Find cot(a/2) + cot(b/2) + cot(c/2), if a + b + c = 180.

Grade:12th pass

1 Answers

Diksha singh
13 Points
5 years ago
If ABC is a triangle 
A + B + C = π 
=> A/2 + B/2 = π/2 - C/2 
=> tan (A/2 + B/2) = tan (π/2 - C/2) 
=> (tan A/2 + tanB/2) / (1 - tan A/2 tan B/2) = cot C/2 
=> (cot A/2 + cot B/2) / (cot A/2 cot B/2 - 1) = cot C/2 
=> cot A/2 + cot B/2 + cot C/2 = cot A/2 cot B/2 cot C/2 

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