Prove each of the following identities:
Consider L.H.S. = (1 + tan θ + cot θ)(sin θ – cos θ)
= sin θ – cos θ + tan θ sin θ – tan θ cos θ + cot θ sin θ – cot θ cos θ
= sin θ – cos θ + tan θ sin θ – sin θ + cos θ – cot θ cos θ
= tan θ sin θ – cot θ cos θ
= (sin2 θ/cos θ) – (cos2 θ/sin θ)
= [(1/cos θ) × (1/cosec2 θ)] – [(1/cosec θ) × (1/sec2 θ)]
= (sec θ/cosec2 θ) – (cosec θ/sec2 θ)
= R.H.S.
Hence, proved.
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