Question

if tanA= cotB, where A&B are acute angle,prove that A+B=90°

Answer 1

Hi
tan A = cot B
i.e 
tan A = tan ( 90 - B )
A = 90 - B
A + B = 90
Hope this answer helps 
Mark it as brainliest if it did thank you

Answer 2

Answer:

Hence proved that the addition of two acute angles A and B in the given equation will be equal to 90°

To Prove:

The addition of two acute angles,

$\angle A + \angle B = 90 ^ { \circ }$

Solution:

Acute angle is a type of angle which "measures" less than 90° and more than 0°, for example the shape and the angle of pizza forms an acute angle. The angle with the measure 0° is not considered as acute angle, it is called as acute angle because it is less than a "right angle".

Given, tan A = cot B

Given both the angles A and B are acute angles,

$\tan A = \tan \left( 90 ^ { \circ } - B \right)$

Since we know that,

$\cot \left( 90 ^ { \circ } - \theta \right) = \tan \theta$

Removing tan on both sides, we get

$\begin{array} { l } { A = 90 ^ { \circ } - B } \\\\ { A + B = 90 ^ { \circ } } \end{array}$

Hence proved the given fact.