Question

How do you simplify `cos(alpha+beta)-cos(alpha-beta)`?

Answer 1

`-2sinalphasinbeta`

Explanation:

Use the following formulas to solve this problem.

•`cos(A + B) = cosAcosB - sinAsinB`

•`cos(A - B) = cosAcosB + sinAsinB`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`cos(alpha + beta) - cos(alpha - beta)`

`=cosalphacosbeta - sin alphasinbeta - (cosalphacosbeta + sinalphasinbeta)`

`=cosalphacosbeta - sinalphasinbeta - cosalphacosbeta - sinalphasinbeta`

`= -2sinalphasinbeta`

Hopefully this helps!