Please verify this identity

$$(1+secx)(1-cosx)=tan^2xcosx\\\\
\begin{array}{rll}
LHS&=&(1+\frac{1}{cosx})(1-cosx)\\\\
&=&1-1-cosx+\frac{1}{cosx}\\\\
&=&\frac{1}{cosx}-cosx\\\\
&=&cosx(\frac{1}{cos^2x}-1)\\\\
&=&cosx(\frac{1-cos^2x}{cos^2x})\\\\
&=&cosx\times\frac{sin^2x}{cos^2x}\\\\
&=&cosx\:tan^2x\\\\
&=&RHS
\end{array}$$

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