sin^4 θ-1/cos^2θ= (sin^2 θ + 1)(sin^2 θ - 1) / cos^2θ
= (sin^2 θ + 1)(sin^2 θ - (sin^θ + cos^2 θ)) / cos^2θ
= (sin^2 θ + 1) * -cos^2 θ / cos^2 θ
= -(sin^2 θ + 1)
= -1 - sin^2 θ
= -1 - (1 - cos^2 θ)
= -2 + cos^2 θ
= cos^2 θ - 2
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Verified answer
sin^4 θ-1/cos^2θ= (sin^2 θ + 1)(sin^2 θ - 1) / cos^2θ
= (sin^2 θ + 1)(sin^2 θ - (sin^θ + cos^2 θ)) / cos^2θ
= (sin^2 θ + 1) * -cos^2 θ / cos^2 θ
= -(sin^2 θ + 1)
= -1 - sin^2 θ
= -1 - (1 - cos^2 θ)
= -2 + cos^2 θ
= cos^2 θ - 2