Question

If tanA= 3/4 and A+B= 90 degree, then what is the value of cotB ?

Answer 1

Answer:

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

Step-by-step explanation:

Given :Tan A= $\frac{3}{4}$ and A+B= 90°

To Find : what is the value of cot B?

Solution:

In ΔABC

∠A+∠B+∠C=180° (Angle sum property of triangle)

Since we are given that ∠A+∠B =90°

So, 90°+∠C=180°

∠C=180°-90°

∠C=90°

So,  ΔABC is a right angled triangle at C

So, $tan \theta = \frac{Perpendicular}{Base}$

We are given that  $tan A =\frac{3}[4}$

So, on comparing

For ∠A

Perpendicular = 3

Base = 4

For ∠B

Base = 3

Perpendicular =4

$cot \theta = \frac{Base}{Perpendicular}$

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

Answer 2

Answer:

$If \:tanA=\frac{3}{4}\:and\\A+B=90\degree ,\:then \\the\:value \: of \: cotB = \frac{3}{4}$

Step-by-step explanation:

$Given \: tanA= \frac{3}{4}--(1)$

$and\\A+B=90\degree$

$\implies B = 90\degree - A$

$\implies cot B = cot\left(90\degree - A\right)$

$\implies cot B = tanA$

/* Since , cot (90°-A)= tanA*/

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

/* From (1) */

Therefore,

$If \:tanA=\frac{3}{4}\:and\\A+B=90\degree ,\:then \\the\:value \: of \: cotB = \frac{3}{4}$

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