Question

If Tan A = cot B where A and B are acute angles 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

$\huge{Emma}$

Given,

Tan A =Cot B

Cot B = Tan (90°-B)

Tan A = Tan (90°-B)

If A , B are acute angles , then A=90°-B

----------->A+B =90°

Hence proved