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L.H.S. = (sin4θ – cos4θ +1) cosec2θ
= [(sin2θ – cos2θ) (sin2θ + cos2θ) + 1] cosec2θ
Using the identity sin2A + cos2A = 1,
= (sin2θ – cos2θ + 1) cosec2θ
= [sin2θ – (1 – sin2θ) + 1] cosec2θ
= 2 sin2θ cosec2θ
= 2 sin2θ (1/sin2θ)
= 2
= RHS
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