Prove:(cosec θ + sin θ)(cosec θ – sin θ) = cot2 θ + cos2 θ

1.	Prove:(cosec θ + sin θ)(cosec θ – sin θ) = cot2 θ + cos2 θ
Answer» Taking L.H.S = (cosec θ + sin θ)(cosec θ – sin θ) On multiplying we get, = cosec² θ – sin² θ = (1 + cot² θ) – (1 – cos² θ) [Using cosec² θ − cot² θ = 1 and sin² θ + cos² θ = 1] = 1 + cot² θ – 1 + cos² θ = cot² θ + cos² θ = R.H.S Hence Proved

Answer»

Taking L.H.S

= (cosec θ + sin θ)(cosec θ – sin θ)

On multiplying we get,

= cosec² θ – sin² θ

= (1 + cot² θ) – (1 – cos² θ) [Using cosec² θ − cot² θ = 1 and sin² θ + cos² θ = 1]

= 1 + cot² θ – 1 + cos² θ

= cot² θ + cos² θ

= R.H.S

Hence Proved

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