alleryStart learning →Which expression equals sin(2x)?
Asin^2 x - cos^2 x
B2 sin x cos x
C2 sin x tan x
Dcos^2 x - sin^2 x
Answer & Solution
Correct answer: B. 2 sin x cos x
1. Put both angles equal in sin(a + b) = sin a cos b + cos a sin b.
2. Both terms become sin x cos x, so their sum is 2 sin x cos x.
3. Hence sin(2x) = 2 sin x cos x.
4. The expression cos^2 x - sin^2 x is a form of cos(2x), so it answers the wrong function.
_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_
Keep practising Trigonometric Identities and Equations
Browse all Trigonometric Identities and Equations questions for B.Sc Mathematics, or explore more Mathematics topics.
Related questions
If a ladder's base is a feet from the wall and its length is 4a feet, how high up the wallSafety rules place a ladder's base 1 foot from the wall for every 4 feet of ladder length.Compared with y = sin t, the graph of y = sin(2t) is which transformation?Solving sin(n t) = c across one turn requires going around the unit circle how many times?Solve cos(2t) = 1/2 on the interval from 0 to 2 pi.Solve 3 cos t + 3 = 2 sin^2 t exactly on the interval from 0 to 2 pi.Solve cos t cos(2t) + sin t sin(2t) = sqrt(3)/2 on the interval from 0 to 2 pi.Solve 2 sin^2 t + sin t = 0 exactly on the interval from 0 to 2 pi.