Question

If A and B are the angles of a right angled triangle ABC, right angled
at C then 1+cot2A =

Answer 1

ABC is right angle ∆
so,
A + B + 90° = 180°
A + B = 90°

A = 90 -B
multiply with 2

2A = 180 -2B

take cot both sides
cot2A = cot(180-2B ) = - cot2B

add 1 both sides

1 + cot2A = 1- cot2B

hence,

(1 + cot2A) = (1 -cot2B)