How i prove this ?

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1 Answer
Apr 16, 2018

Please see below.

Explanation:

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)