trigonometry

tan (x) sin (x) + sec (x) cos2 (x)
I am assuming you mean

tan (x) sin (x) + sec (x) cos ²(x)

= sinx/cosx * sinx + 1/cosx * cos ²(x)

= sin ²x/cosx + cosx

= (sin ²x + cos ²x) / cosx

= 1 / cosx

= sec x