Use the fundamental trigonometric id's to simplify the equation

(tanx + 1)^2 cosx          expand

(tan^2x + 2tanx + 1) cosx

(tan^2x + 1  + 2tanx) cos x      re-order inside the parentheses

........... tan^2x + 1   = sec^2x ..........

(sec^2x + 2tanx) cosx          put everything in terms of sine, cosine        

( 1/cos^2x   +  2 sinx / cos x )  cosx        

 Distribute the cosx acroos the terms in the parentheses

( 1/cos x  +  2 sin x)

secx  + 2sinx