Prove that sin-cos+1 = cosec
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Answer:
Solution :
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 = RHS