Tan -cosec×sec(1-cos²)=0
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Tan θ - csc θ * sec θ * ( 1 - cos² θ )
(we know sin² θ + cos² θ = 1 ⇒ sin² θ = 1 - cos² θ)
= Tan θ - csc θ * sec θ * sin² θ ( sin θ = 1 / csc θ )
= Tan θ - sec θ * sin θ ( sec θ * sin θ = sin θ / cos θ = tan θ )
= Tan θ - ( Tan θ )
= 0
Hence proven
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