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

( tan theta - 1/cos theta)^2

=[ (sin theta/cos theta -1 / cos theta] ^2

= (sin theta -1 /cos theta) ^2

= (sin theta -1) ^2 / cos^2 theta

= ( sin theta-1) ^2/ ( 1- sin^2 theta0

= (sin theta-1) ( sin theta-1)/ ( 1+ sin theta) ( 1-sin theta)

= sin theta -1/ sin theta +1

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