Question

sin a + b is equal to root 3 by 2 and cos a minus b is equal to 1 by root 2 find a,b​

Answer 1

Answer:

A=60 & B=30

Step-by-step explanation:

We have Sin (A+B)=1 

(A+B)=sin-1 1

We know sin-1 1 = 90 

A+B=90 --------(1) 

Cos (A-B) =√3/2 

A-B=cos-1 √3/2 

We know cos-1 √3/2=30 

A-B=30 -----------(2) 

Solve (1) & (2) 

A+B=90

  A-B=30 add  2A=120

A=60 & B=30

Answer 2

$Given \: Sin(A+B) = \frac{\sqrt{3}}{2}$

$\implies Sin(A+B) = sin \: 60\degree$

$\implies A + B = 60 \degree \: --(1)$

$and \: Cos(A-B) = \frac{1}{\sqrt{2}}$

$\implies Cos (A-B) = cos \: 45\degree$

$\implies A - B = 45\degree \: --(2)$

/* Add Equations (1) and (2) , we get */

$2A = 105$

$\implies A = \frac{105}{2}$

$\implies A = 52.5$

/* Put A = 52.5 in equation (1), we get */

$\implies 52.5 + B = 60$

$\implies B = 60 - 52.5= 7.5 \degree$

Therefore.,

$\green { A = 52.5\degree \:and \: B = 7.5 \degree }$

•••♪