Question

If sin(A+B) = cos (A-B)=√3/2 and A and B are acute angles.find the values of A and B???

Answer 1

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°

Answer 2

Answer:

Step-by-step explanation:

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°