If sin(A+B) = cos (A-B)=√3/2 ;A is greater than B and A and B are ac

1.	If sin(A+B) = cos (A-B)=√3/2 ;A is greater than B and A and B are acute angles.find the values of A and B??? Please answer its urgent!!
Answer» ANSWER: sin(A+B)=cos(A-B)=√3/2 ∴, sin(A+B)=√3/2 or, sin(A+B)=sin60° or, A+B=60° --------------(1) cos(A-B)=√3/2 or, cos(A-B)=cos30° or, A-B=30° ---------------(2) Adding (1) and (2) we GET, 2A=90° or, A=45° Putting in (1) we get, 45°+B=60° or, B=15° ∴, A=45°, B=15° Step-by-step EXPLANATION:

If sin(A+B) = cos (A-B)=√3/2 ;A is greater than B and A and B are acute angles.find the values of A and B??? Please answer its urgent!!

Answer»

sin(A+B)=cos(A-B)=√3/2

∴, sin(A+B)=√3/2

or, sin(A+B)=sin60°

or, A+B=60° --------------(1)

cos(A-B)=√3/2

or, cos(A-B)=cos30°

or, A-B=30° ---------------(2)

Adding (1) and (2) we GET,

2A=90°

or, A=45°

Putting in (1) we get,

45°+B=60°

or, B=15°

∴, A=45°, B=15°

Step-by-step EXPLANATION: