Question

If A+B=45 then find (cotA-1)(cotB-1)

Answer 1

Trignometric ratio of compound angle.

The algebric sum of two or more angles is called a compound angle.

A+B = 45

Apply 'cot' on both sides,

cot(A+B) = cot 45

cot A cot B -1 / cot B + cot A = 1

cot A cot B -1 = cot A + cot B

cot A cot B - cot A - cot B = 1

Now,

(cot A-1)(cotB-1) =cotAcotB-cotA-cotB+1

(cot A-1)(cotB-1)=2

Hence proved!