I would write:

\(\displaystyle \tan(x)\cos\left(1^{\circ}\right)+\sin\left(1^{\circ}\right)=\frac{\sin(x)\cos\left(1^{\circ}\right)+\cos(x)\sin\left(1^{\circ}\right)}{\cos(x)}\)

Applying the angle-sum identity for sine, we may write:

\(\displaystyle \tan(x)\cos\left(1^{\circ}\right)+\sin\left(1^{\circ}\right)=\frac{\sin\left(x+1^{\circ}\right)}{\cos(x)}\)