Question

If A + B + C = 180°, then `sum tan  A/2 tan  B/2` is ______.

विकल्प

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Answer 1

If A + B + C = 180°, then `sum tan  A/2 tan  B/2` is 1.

Explanation:

Given, A + B

`\implies A/2 + B/2 = 90^circ - C/2`

`\implies tan(A/2 + B/2) = tan(90^circ - C/2)`

`\implies (tan  A/2 + tan  B/2)/(1 - tan  A/2 tan  B/2) = cot  C/2`

`\implies (tan  A/2 + tan  B/2) tan  C/2 = 1 - tan  A/2  tan  B/2`

`\implies tan  A/2 tan  B/2 + tan  B/2 tan  C/2 + tan  A/2  tan  C/2` = 1