Question

If A is less than B, sin A= cos B, then find cot B and tan A

Answer 1

$\Huge{\underline{\underline{\mathfrak{Answer \colon}}}}$

Given

• A is less than B : A < B

• sin A = cos B

We know that,

sin30 = cos60 = 1/2

Here,

A = 30° and B = 60°

and, A,B < π/2

To find:

cot B and tan A

Now,

tan A = tan30° = 1/√3

Also,

cot B = cot60° = 1/√3

Thus,cotB = tanA = 1/√3

Answer 2

$\huge{\bold{\underline{\underline{Answer:-}}}}$

$\large{\bold{\underline{\underline{Given:-}}}}$

•$\large\sf\ A\: is \: less \: than \: B$

•$\large\sf\ SinA= SinB$

$\large{\bold{\underline{\underline{To find:-}}}}$

•$\large\sf\ CotB =?$

•$\large\sf\ TanA=?$

$\large{\bf{\underline{\underline{Step-by-step-explanation:-}}}}$

Since,According to Trigonometric ratios;

$\large\purple{\boxed{\sf Sin30 = Cos60=\frac{1}{2} ---(eq1.) }}$

Here,it is given that ;

$\large\purple{\boxed{\sf SinA=SinB ----(eq2.) }}$

from equation 1 and 2 ,we can conclude that ;

$\large\implies\bf\ A=30$

$\large\implies\bf\ B=60$

•°•Now ,

we have to find ;

$\large\sf\ CotB =?$

So,

$\large\implies\sf\ CotB =Cot60$

$\large\implies\sf\ CotB= \frac {1}{ \sqrt 3}$

•°•Now,we have to find

$\large\implies\sf\ TanA=?$

So,

$\large\implies\sf\ TanA= Tan30$

$\large\implies\sf\ TanA= \frac {1}{ \sqrt 3}$

$\mathbb\pink{Thanks...}$