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Question
If A = 35°, B = 15° and C = 40°, then tan A tan B + tan B tan C + tan C tan A is equal to ______.
Options
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MCQ
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Solution
If A = 35°, B = 15° and C = 40°, then tan A tan B + tan B tan C + tan C tan A is equal to 1.
Explanation:
∵ tan (A + B + C) = `([tan A + tan B + tan C - tan A tan B tan C])/([1 - tan A tan B - tan B tan C - tan C tan A])`
`\implies` tan (90°) = `(tan A + tan B + tan C - tan A tan B tan C)/(1 - tan A tan B - tan B tan C - tan C tan A)`
∴ tan A tan B + tan B tan C + tan C tan A = 1
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Conversion Formulae in Trigonometry
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