Answer:
steps below
Step-by-step explanation:
Step 1: Cot A / (1+cot A) * Cot B / (1+cot B )
= (Cot A * Cot B) / ((1+cot A) *(1+cot B ))
= (Cot A * Cot B) / (1+cot A+cot B+cot A cot B)
= (Cot A * Cot B) / ((1+cot A+cot B)+ (cot A cot B)) : a
Step 2: (cot A * cot B -1) / (cot A + cot B) = cot (A+B) = cot 225° = 1 (formula)
cot A * cot B -1 = cot A + cot B
cot A * cot B = 1 + cot A + cot B (substitute a)
Step 3:
Cot A / (1+cot A) * Cot B / (1+cot B )
= (Cot A * Cot B) / ((cot A * cot B)+ (cot A * cot B))
= (Cot A * Cot B) / (2 * (cot A * cot B))
= 1 / 2
= 0.5
