we know that
if angle A=45°
then
angle C is also 45°
therefore
if BC=6
AB is also 6
applying the Pythagorean theorem
AC²=AB²+BC²--------> AC²=6²+6²------> AC²=72------> AC=6√2
cos 45=6/(6√2)--------> cos 45=1/√2
the answer is the option B
cos 45=1/√2
