Prove trigonometric identity and how to have ideas

This is the identity:

${\mathrm{cos}}^{2}(a)-{\mathrm{cos}}^{2}(b)=\frac{{\mathrm{tan}}^{2}(b)-{\mathrm{tan}}^{2}(a)}{(1+{\mathrm{tan}}^{2}(a))\cdot (1+{\mathrm{tan}}^{2}(b))}$

This is the identity:

${\mathrm{cos}}^{2}(a)-{\mathrm{cos}}^{2}(b)=\frac{{\mathrm{tan}}^{2}(b)-{\mathrm{tan}}^{2}(a)}{(1+{\mathrm{tan}}^{2}(a))\cdot (1+{\mathrm{tan}}^{2}(b))}$