Question

If A+B = 45° , then find (CotA-1) (CotB-1).

(A) 1

(B) 2

(C) 4

(D) 3

Answer 1

Hii friend,

A+B = 45°

B = 45°-A

(Cot A - 1) ( Cot B -1)

= (1/Tan A - 1 ) ( 1/Tan B - 1)

= (1/Tan A-1) ( 1/ Tan (45-A) -1)

= (1-Tan A/ Tan A ) ( 1/Tan45° - Tan A -1)

= (1/Tan A / Tan A ) ( 1+Tan45° Tan A -1 / Tan 45°- Tan A )

= (1-Tan A / Tan A ) ( 1+Tan A -1/ 1-Tan A)

= (1-Tan A / Tan A ) ( 2 Tan A / 1- Tan A )

= 2

Therefore,

Option (B) is right answer.

HOPE IT WILL HELP YOU..... :-)

Answer 2

The right answer is (B)