alleryStart learning →Which quotient is the double-angle formula for tangent?
A2 tan x / (1 + tan^2 x)
Btan x / (1 - tan^2 x)
C2 tan x / (1 - tan^2 x)
D2 tan x / (tan^2 x - 1)
Answer & Solution
Correct answer: C. 2 tan x / (1 - tan^2 x)
1. Set both angles equal in tan(a + b) = (tan a + tan b) / (1 - tan a tan b).
2. The numerator becomes tan x + tan x = 2 tan x.
3. The denominator becomes 1 - tan x times tan x, that is 1 - tan^2 x.
4. So tan(2x) = 2 tan x / (1 - tan^2 x).
5. The version with tan^2 x - 1 in the denominator is the negative of the correct value.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.3 Double-Angle, Half-Angle, and Reduction Formulas_
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