Given that, `" "cosalpha+cosbeta=0=sinalpha+sinbeta`
`rArr" "(cosalpha+cosbeta)^(2)-(sinalpha+sinbeta)^(2)=0`
`rArr" "cos^(2)alpha-sin^(2)beta+2cosalphacosbeta-sin^(2)alpha-sin^(2)beta-2sinalphasinbeta= 0`
`rArr" "cos^(2)alpha-sin^(2)alpha+cos^(2)beta-sin^(2)beta=2(sinalphasinbeta-cosalphacosbeta)` ` rArr" "cos2alpha+cos2beta=-2cos(alpha+beta)" "` Hence proved.
