Question

Illustration 7. If A + B = 45°, show that (cot A - 1)(cot B - 1) = 2.

JEE/Engineering Exams

Maths

Solution

150

5.0 (1 ratings)

( cot (A+B)=(operatorname{Cot} A C O t B-1) /(C O t A+C O t B) ) We know...... ( cot (45)=1 ) so, ( 1=(cot A cot B-1) /(cot A+cot B) ) ( operatorname{Cot} A operatorname{Cot} B-1)=(operatorname{Cot} A+operatorname{Cot} B) ) ( operatorname{Cot} A operatorname{Cot} B-cot A-cot B=1 ) adding 1 to both sides.....we get ( (cot A-1)(cot B-1)=2 ldots ldots ) proved