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Question
If A + B = C = 180°, then the value of `cot A/2 + cot B/2 + cot C/2` will be ______.
Options
`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`
MCQ
Fill in the Blanks
Solution
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`
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Factorization Formulae - Trigonometric Functions of Angles of a Triangle
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