Prove that (tanθ - 1/cosθ)^2 = sinθ-1/sinθ+1

(tanθ - 1/cosθ)^2 = tan^2 θ - 2 tanθ/cos θ + 1/cos^2 θ

= sin^2 θ / cos^2 θ - 2 sinθ/cosθ/cosθ + 1/cos^2 θ

= (sin^2 θ - 2sinθ + 1) / cos^2 θ

= (sinθ - 1)(sinθ - 1) / 1-sin^2 θ

= (sinθ - 1)(sinθ - 1) / (1+sinθ)(1-sinθ) = 1-sinθ/1+sinθ

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