In a triangle ABC, Cot A/2 +Cot B/2 +Cot C/2 is equal to
In a triangle ABC, Cot A/2 +Cot B/2 +Cot C/2 is equal to
AyishaShadha , 6 Years ago
Grade 12th pass
Trigonometry> In a triangle ABC, Cot A/2 +Cot B/2 +Cot ...
1 AnswersRAHUL ROHILLA
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
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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