alleryStart learning →Substituting tan x = -3/4 into the double-angle formula for tangent gives which value for tan(2x)?
A24 / 7
B-3 / 2
C-7 / 24
D-24 / 7
Answer & Solution
Correct answer: D. -24 / 7
1. Use tan(2x) = 2 tan x / (1 - tan^2 x) with tan x = -3/4.
2. The numerator is 2 times (-3/4) = -3/2.
3. The square is (-3/4)^2 = 9/16, so the denominator is 1 - 9/16 = 7/16.
4. Dividing gives (-3/2) times (16/7).
5. That equals -48/14, which reduces to -24/7.
6. The option -3/2 is only the numerator, so it stops one step short.
7. The option -7/24 inverts the answer by dividing the wrong way round.
_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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