Answer
cos 45° = 1
Work Step by Step
$\cot$ 45$^{\circ}$
We must find side x of the 45$^{\circ}$ - 45$^{\circ}$ Right Triangle.
Pythagorean Theorem: c$^{2}$ = a$^{2}$ + b$^{2}$
x$^{2}$ = 1$^{2}$ + 1$^{2}$
x$^{2}$ = 2
x = $\sqrt2$
Now consider the triangle from the perspective of a 45$^{\circ}$ angle.
Hypotenuse = $\sqrt2$
Opposite = 1
Adjacent = 1
$\cot$ 45$^{\circ}$ = $\frac{Adjacent}{Opposite}$ = $\frac{1}{1}$ = 1
Therefore:
cos 45° = 1
