alleryStart learning →Write tan(pi/9) in terms of its cofunction.
Acot(2 pi / 18)
Bcot(11 pi / 18)
Ccot(7 pi / 9)
Dcot(7 pi / 18)
Answer & Solution
Correct answer: D. cot(7 pi / 18)
1. The cofunction identity for tangent is tan x = cot(pi/2 - x).
2. Here x = pi/9, so the answer is cot(pi/2 - pi/9).
3. Write both fractions over 18: pi/2 = 9 pi / 18 and pi/9 = 2 pi / 18.
4. Subtracting gives 9 pi / 18 - 2 pi / 18 = 7 pi / 18.
5. So tan(pi/9) = cot(7 pi / 18).
6. The option cot(2 pi / 18) is just cot(pi/9) and confuses the angle with its complement.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.2 Sum and Difference Identities_
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