Question

Prove that [sin^4-cos^4+1]cosec^2=2

Answer 1

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Answer 2

L.H.S. = (sin4θ – cos4θ +1) cosec2θ

= [(sin2θ – cos2θ) (sin2θ + cos2θ) + 1] cosec2θ

= (sin2θ – cos2θ + 1) cosec2θ [Because sin 2θ + cos2θ =1]

= 2sin2θ cosec2θ [Because 1– cos 2θ = sin2θ ]

= 2

∴ LHS = RHS

HENCE PROVED

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