alleryStart learning →Which quotient is the difference formula for tangent?
A(tan a - tan b) / (1 - tan a tan b)
B(tan a - tan b) / (1 + tan a tan b)
C(tan a + tan b) / (1 - tan a tan b)
D(tan a + tan b) / (1 + tan a tan b)
Answer & Solution
Correct answer: B. (tan a - tan b) / (1 + tan a tan b)
1. For a difference of angles the numerator carries the difference of the tangents.
2. The denominator is 1 plus the product of the tangents.
3. So tan(a - b) = (tan a - tan b) / (1 + tan a tan b).
4. The version with a minus sign in the denominator is the sum formula, where the numerator also carries a plus sign.
_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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