How do you simplify $cos (α + β) - cos (α - β)$ $cos(alpha+beta)-cos(alpha-beta)$ ?

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How do you simplify $cos (α + β) - cos (α - β)$ $cos(alpha+beta)-cos(alpha-beta)$ ?

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Answer 1 · 2016-12-17T14:56:58

$- 2 sin α sin β$ $-2sinalphasinbeta$

Explanation:

Use the following formulas to solve this problem.

• $cos (A + B) = cos A cos B - sin A sin B$ $cos(A + B) = cosAcosB - sinAsinB$

• $cos (A - B) = cos A cos B + sin A sin B$ $cos(A - B) = cosAcosB + sinAsinB$

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

$cos (α + β) - cos (α - β)$ $cos(alpha + beta) - cos(alpha - beta)$

$= cos α cos β - sin α sin β - (cos α cos β + sin α sin β)$ $=cosalphacosbeta - sin alphasinbeta - (cosalphacosbeta + sinalphasinbeta)$

$= cos α cos β - sin α sin β - cos α cos β - sin α sin β$ $=cosalphacosbeta - sinalphasinbeta - cosalphacosbeta - sinalphasinbeta$

$= - 2 sin α sin β$ $= -2sinalphasinbeta$

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How do you simplify $cos (α + β) - cos (α - β)$ $cos(alpha+beta)-cos(alpha-beta)$ ?

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