Question

sin(A+B)=√3/2=cos(A-B). Find A and B.

Answer 1

hence value of A=45 ,and value of B=15

Answer 2

Hello users ...

We know that:
sin 60° = √3 / 2

And
cos 30° = √3 / 2

Solution:-
here,
Given that;
sin (A + B) = √3 / 2 

=> sin(A + B) = sin 60°

=> A + B = 60° ......... (1.) 

And
cos (A-B) =√3 / 2

=> cos ( A - B) = cos 30°

⇒   A-B = 30°.......(2)

Now, solving ....
by adding equation (1.) and (2.)
we get
(A + B) + (A - B) = 60° + 30°

=> 2A = 90°
=> A = 90° /2 = 45°

By subtracting (2.) from (1.)
we get
(A + B) - ( A - B) = 60° - 30°

=> A + B - A + B = 30°

=> 2B = 30°
=> B = 30° / 2 = 15° 

Hence;
∠A = 45°
And
∠B = 15° Answer 

Hope it helps :)