Question

Given that angle A is 120°,if A,B,C are the interior angles of triangle ABC,then find the value of tanB+C/2 + tanA/2 .

Answer 1

it is given that A, B and C are the interior angles of triangle ABC and ∠A = 120°

we have to find the value of tan(B + C)/2 + tanA/2

we know, sum of all angles of triangle = 180°

⇒ A + B + C = 180°

⇒120° + B + C = 180°

⇒B + C = 60°

now tan(B + C)/2 = tan(60°)/2 = tan30° = 1/√3

tanA/2 = tan60°/2 = tan30° = 1/√3

so, tan(B + C)/2 + tanA/2 = 1/√3 + 1/√3 = 2/√3

therefore, tan(B + C)/2 + tanA/2 = 2/√3

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Answer 2

Answer:

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