alleryStart learning →The formula for cos a cos b is obtained by combining the two cosine formulas in which way?
ABy adding them, then dividing by 2
BBy subtracting them, then dividing by 2
CBy multiplying them, then taking a root
DBy adding them, then dividing by 4
Answer & Solution
Correct answer: A. By adding them, then dividing by 2
1. Write cos(a - b) = cos a cos b + sin a sin b and cos(a + b) = cos a cos b - sin a sin b.
2. Adding the two equations cancels the sine terms and leaves 2 cos a cos b on one side.
3. The other side becomes cos(a - b) + cos(a + b).
4. Dividing by 2 isolates the product, giving cos a cos b = (1/2)[cos(a - b) + cos(a + b)].
5. Subtracting instead of adding would cancel the cosine terms and produce the formula for sin a sin b.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.4 Sum-to-Product and Product-to-Sum 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.