Question

If A + B = C = 180°, then the value of `cot  A/2 + cot  B/2 + cot  C/2` will be ______.

पर्याय

• `2 cot  A/2 cot  B/2 cot  C/2`

• `4 cot  A/2 cot  B/2 cot  C/2`

• `cot  A/2 cot  B/2 cot  C/2`

• `8 cot  A/2 cot  B/2 cot  C/2`

Answer 1

If A + B = C = 180°, then the value of `cot  A/2 + cot  B/2 + cot  C/2` will be `underlinebb(cot  A/2 cot  B/2 cot  C/2)`.

Explanation:

A + B + C = 180°

∴ `A/2 + B/2 = 90^circ - C/2`

∴ `cot(A/2 + B/2) = cot(90^circ - C/2)`

or `(cot  A/2 . cot  B/2 - 1)/(cot  B/2 + cot  A/2) = tan  C/2 = 1/(cot  C/2)`

or `(cot  A/2 cot  B/2 - 1) cot  C/2 = cot  B/2 + cot  A/2 + cot  A/2 . cot  B/2 . cot  C/2`

= `cot  C/2 + cot  B/2 + cot  A/2`