alleryStart learning →Which equation is one of the two quotient identities?
Acot x = sin x / cos x
Bcot x = cos x / sin x
Ctan x = cos x / sin x
Dsec x = sin x / cos x
Answer & Solution
Correct answer: B. cot x = cos x / sin x
1. The quotient identities are tan x = sin x / cos x and cot x = cos x / sin x.
2. Cotangent is the ratio of cosine to sine, so cot x = cos x / sin x is correct.
3. The options that put sine over cosine for cotangent, or cosine over sine for tangent, invert the ratio.
4. Secant is a reciprocal, not a quotient of sine and cosine, so that option names the wrong family.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.1 Solving Trigonometric Equations with Identities_
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