Verify: (cosx)(tan^2x) + cosx = secx

We know that tanx = sinx/ cosx and  secx =1/cosx. And the trigonometric identity, (sinx)^2+(cosx)^2 = 1

Left side:

cosx(tanx)^2 +cosx = cosx(sinx/cosx)^2+cosx = (sinx)^2/cosx+cosx = (sinx)^2 / cosx + cos x*cosx/cosx = [(sinx)^2+(cosx)^2]/cosx = 1/cosx =secx which is the term on RHS.