Prove the following with the help of identities:

sec θ (1 – sin θ) (sec θ + tan θ) = 1

Taking L.H.S we get,

sec θ (1 – sin θ) (sec θ + tan θ)

⇒ (sec θ – sec θ.sin θ) (sec θ + tan θ)

⇒ (sec θ – tan θ) (sec θ + tan θ)

Using the identity: (a + b) (a – b) = a² – b²

⇒ sec² θ – tan² θ

= 1

= R.H.S

Hence, proved

Note: sin² θ + cos² θ = 1

sec² θ – tan² θ = 1

cosec² θ – cot² θ = 1