Question

If tan A = cot B, prove that A + B = 90°

Answer 1

    tan A = cot B ------------ ( eq. i)   { given }

also, tan A = cot ( 90 - A ) ------------ ( eq.ii )   { complimentary angle }

From eq. i & ii -
  cot B = cot ( 90°- A )
⇒ B = 90° - A.
⇒ 90 ° = A + B.
⇒ A + B = 90 °. [ PROVED ] .

Answer 2

tan A = cot B -------- 1
tan (90°-B)  = cot B ----- 2
By equating 1 and 2
tan A = tan (90°-B)
A=90°-B
Therefore, A+B = 90°
Hence, It is proved.