Use a suitable substitution to show these integrals are equal

Question

$$\int\frac{\cos(\tan^{2}t)}{1+t^2}dt=\int\cos(t^2)dt$$

Please help, I have tried substituting in different values such as $u = \tan^2(t)$, however, I am not getting very far with it.

Answer 1

Let $$u=\tan t, du=(1+\tan ^2t) dt$$ and then change the dummy variable back to $t$