Concept: 1 Mark
Application: 1 Mark
We have
=cosec θ(cosec θ−1)+cosec θ(cosec θ+1)
=cosec θ(cosec θ+1)+cosec θ(cosec θ−1)(cosec2 θ−1)
=2 cosec2 θ(1+cot2 θ−1) [∵cosec2 θ=1+cot2 θ]
=2 cosec2 θcot2 θ
=2 cosec2 θ tan2 θ
=2×1sin2 θ×sin2 θcos2 θ
=2cos2 θ
=2 sec2 θ