Question

if A+B = 90 and tan A = $\frac{3}{4}$ , find the value of cot B

Answer 1

Answer:

cotB=$\frac{3}{4}$

Step-by-step explanation:

A+B=90

A=90-B ------------1

Tan A=$\frac{3}{4}$

Tan (90-B)=$\frac{3}{4}$

Cot B=$\frac{3}{4}$

Answer 2

Answer:

$\large\bold\red{\frac{3}{4}}$

Step-by-step explanation:

Given,

A + B = 90

=> tan ( A + B ) = tan 90

$= > \frac{ \tan(A) + \tan( B) }{1 - \tan(A) \tan( B ) } = \frac{1}{0} \\ \\ = > 1 - \tan( A ) \tan( B) = 0 \\ \\ = > \tan( A ) \tan( B ) = 1$

But,

it is given that,

tan A = $\frac{3}{4}$

Thus,

putting the values,

we get,

$= > \frac{3}{4} \times \tan( B ) = 1 \\ \\ = > \tan( B ) = \frac{4}{3}$

But,

we know that,

$\tan(x) = \frac{1}{ \cot(x) }$

Hence,

$\bold{ \cot( B ) = \frac{3}{4} }$