Question

If tan A =cotB, prove that A+B=90°

Answer 1

tan A = cot B
tan A=cot(90-B)
A=90-B
A+B =90

Answer 2

Here is your answer :

tan A = cot B ( given ) -----(i)

Also, tan A = cot ( 90° - A ) -----(ii) [ complementary angle ]

From (i) & (ii) ,

==> cot B = cot ( 90° - A )

==> B = 90° - A

==> A + B = 90°

PROVED