Verify the identity.? cos(α - β) - cos(α + β) = 2 sin α sin β

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1 Answer
Jim G.
Mar 28, 2018

#"see explanation"#

Explanation:

#"using the "color(blue)"trigonometric identities"#

#•color(white)(x)cos(x+-y)=cosxcosy∓sinxsiny#

#"cinsider the left side"#

#rArrcos(alpha-beta)=cosalphacosbeta+sinalphasinbeta#

#rArrcos(alpha+beta)=cosalphacosbeta-sinalphasinbeta#

#rArrcancel(cosalphacosbeta)+sinalphasinbetacancel(-cosalphacosbeta)+sinalphasinbeta#

#=2sinbetasinalpha=" right side "rArr"verified"#

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