(1+cotθ−cosecθ)(1+tanθ+secθ)
=1+tanθ+secθ+cotθ+cotθtanθ+cotθsecθ−cosecθ−cosecθtanθ−cosecθsecθ
=1+tanθ+secθ+cotθ+(1tanθ×tanθ)+(cosθsinθ×1cosθ)−cosecθ−(1sinθ×sinθcosθ)−cosecθsecθ
=1+tanθ+secθ+cotθ+1+1sinθ−cosecθ−1cosθ−cosecθsecθ
=1+tanθ+secθ+cotθ+1+cosecθ−cosecθ−secθ−cosecθsecθ
=2+tanθ+cotθ−secθcosecθ
=2+sinθcosθ+cosθsinθ−1sinθcosθ
=2sinθcosθ+sin2θ+cos2θ−1sinθcosθ=2sinθcosθsinθcosθ=2