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tan(θ+1)tan(θ-1)
=[sin(θ+1)/cos(θ+1)][sin(θ-1)/cos(θ-1)]
=[sin(θ+1)sin(θ-1)]/[cos(θ+1)cos(θ-1)]
=(-½)[cos(θ+1+θ-1)-cos(θ+1-θ+1)]/{(½)[cos(θ+1+θ-1)+cos(θ+1-θ+1)]}
=-[cos(2θ)-cos2]/[cos(2θ)+cos2]
=-[cos(2θ)-2cos(2θ)]/[cos(2θ)+2cos(2θ)]
=cos(2θ)/[3cos(2θ)]
=⅓
=[sin(θ+1)/cos(θ+1)][sin(θ-1)/cos(θ-1)]
=[sin(θ+1)sin(θ-1)]/[cos(θ+1)cos(θ-1)]
=(-½)[cos(θ+1+θ-1)-cos(θ+1-θ+1)]/{(½)[cos(θ+1+θ-1)+cos(θ+1-θ+1)]}
=-[cos(2θ)-cos2]/[cos(2θ)+cos2]
=-[cos(2θ)-2cos(2θ)]/[cos(2θ)+2cos(2θ)]
=cos(2θ)/[3cos(2θ)]
=⅓
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