Question

if A+B+C=180° prove then TAN A/2 TANnB/2 +TAN B/2 TAN C/2 +TAN C/2 TANA/2 =1​

Answer 1

Answer:

Solution:

Given,

A + B + C = 180°

(A/2) + (B/2) + (C/2) = 90°

(A/2) + (B/2) = 90° – (C/2)

Taking “tan” on both sides,

tan(A/2 + B/2) = tan(90° – C/2)

[tan A/2 + tan B/2]/ [1 – tan A/2 tan B/2] = cot C/2

[tan A/2 + tan B/2]/ [1 – tan A/2 tan B/2] = 1/tan C/2

tan C/2 [tan A/2 + tan B/2] = 1 – tan A/2 tan B/2

tan A/2 tan C/2 + tan B/2 tan C/2 + tan A/2 tan B/2 = 1

Thus, ∑tan A/2 tan B/2 = 1

Step-by-step explanation: