InterviewSolution
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InterviewSolution
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If `cos(alpha+beta)*sin(gamma+delta)=cos(alpha-beta)*sin(gamma-delta),`prove that `cotalphacotbetacotgamma=cotdelta` |
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Answer» `cos(alpha+beta)sin(gamma+delta) = cos(alpha-beta)sin(gamma-delta)` `cos(alpha+beta)/cos(alpha-beta) = sin(gamma-delta)/sin(gamma+delta)` Using componendo and dividendo, `=>(cos(alpha+beta)+cos(alpha-beta))/ (cos(alpha+beta)-cos(alpha-beta))= (sin(gamma-delta)+sin(gamma+delta))/(sin(gamma-delta)-sin(gamma+delta))` `=>(2cosalphacosbeta)/(-2sinalphasinbeta) = (2singammacos(-delta))/(2sin(-delta)cosgamma)` `=>(cosalphacosbeta)/(-sinalphasinbeta) = (singammacosdelta)/(-sindeltacosgamma)` `=>cotalphacotbeta = cotdelta/cotgamma` `=>cotalphacotbeta cotgamma = cot delta` |
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