Question

verify: cos(x)+sin(x)tan(x)=sec(x)

Answer 1

Let's work on the left side of that possible identity.

cosx + sinx*tanx = cosx + sin^2x /cosx
= cosx + (1 - cos^2x)/cosx
= cosx + 1/cosx - cosx = 1/cosx = secx

That agrees with the right side, so the identity is true.