Sin and Cos

$\sin \alpha = \cos \alpha$

$\implies \tan \alpha = 1$

$\implies \alpha=n \pi+\dfrac{\pi}{4}$

So there are infinitely many n, $\implies$ Answer is infinite.

let alpha be called u. (to avoid latex ; i also not divide, to spread cases cos=0, and tan indefinite, and explanation needed)

sin u = cos u means :

sin u = sin (pi/2 - u)

2 possibilities : u = pi/2 - u OR (pi - u) = pi/2 -u (second is impossible)

First possibility gives 2u = pi/2 (+-2pi n) So u = pi/4 (+-pi n)

In [-pi/2 ; +pi] only one possibility ; in |R, infinity of denombrable possibilities.