Question

If a+b = 225, then cot a/(1 + cot a )*cot b/(1+cot b) =

Answer 1

We know that
cot(a+b) = (cot a cot b - 1) / (cot b+cot a)

So, we get
cot 225 = (cot a cot b - 1) / (cot b+cot a)
We know tjat value of cot 225=1, so
1 = (cot a cot b - 1) / (cot b+cot a)
We can write
cot b+cot a = cot a cot b - 1 .......... (i)

Then, we get
cot a / (1+cot a) * cot b / (1+cot b)
= (cot a cot b )/ (1+cot a+cot b+cot a cot b)
Substituting (i), we get
= cot a cot b / (1+cot a cot b-1+cot a cot b)
= cot a cot b / 2 cot a cot b = 1/2