alleryStart learning →Which expression equals sin^2 x by the reduction formula?
A(1 + cos(2x)) / 2
B(1 - cos(2x)) / 2
C(1 - sin(2x)) / 2
D(1 - cos(2x)) / 4
Answer & Solution
Correct answer: B. (1 - cos(2x)) / 2
1. Start from the double-angle form cos(2x) = 1 - 2 sin^2 x.
2. Rearranging gives 2 sin^2 x = 1 - cos(2x).
3. Dividing by 2 gives sin^2 x = (1 - cos(2x)) / 2.
4. The form with a plus sign is the reduction formula for cos^2 x, which comes from cos(2x) = 2 cos^2 x - 1.
5. Dividing by 4 would break the check at x = pi/2, where sin^2 x must equal 1.
_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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