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