Recall that secx is the reciprocal of cosx.
Also, recall the property:
[tex]cos^{2}x + sin^{2}x = 1[/tex]
[tex]\therefore cos^{2}x = 1 - sin^{2}x[/tex]
Thus, we can rewrite the equation as:
[tex]secx tanx (1 - sin^{2}x) = secx tanx cos^{2}x[/tex]
[tex]= tanx cosx[/tex]
[tex]= \frac{sinx}{cosx} \cdot cosx[/tex]
[tex]= sinx[/tex]
