Prove that (cosec theta+sin theta)(cosec theta-sin theta)=cot square theta+cos square theta
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consider the identities,
cosec² θ = 1+cot² θ
sin² θ = 1 - cos² θ
(cosec θ+sin θ)(cosec θ-sin θ)
= cosec² θ - sin² θ
= 1+cot² θ - (1 - cos² θ)
= cot² θ - cos² θ
cosec² θ = 1+cot² θ
sin² θ = 1 - cos² θ
(cosec θ+sin θ)(cosec θ-sin θ)
= cosec² θ - sin² θ
= 1+cot² θ - (1 - cos² θ)
= cot² θ - cos² θ
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