How i prove this ?

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Answer 1 · 2018-04-16T09:14:24

Please see below.

As #sin(alpha+-beta)=sinalphacosbeta+-cosalphasinbeta#

and #cos(alpha+-beta)=cosalphacosbeta∓sinalphasinbeta#

Hence #(sin(alpha+beta)-2sinalphacosbeta)/(2sinalphasinbeta+cos(alpha+beta))#

= #(sinalphacosbeta+cosalphasinbeta-2sinalphacosbeta)/(2sinalphasinbeta+cosalphacosbeta-sinalphasinbeta)#

= #(sinbetacosalpha-cosbetasinalpha)/(cosbetacosalpha+sinbetasinalpha)#

= #sin(beta-alpha)/cos(beta-alpha)#

= #tan(alpha-beta)#