Question

If sin(A+B)=√3/2 and cos(A-B)=√3/2, then find A and B. Hence find the value of tan(A+B)+tan(A-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°


tan(A+B)+tan(A-B) = tan (45+15) + tan(45-15)

= tan 60 + tan 30

= 1/√3 + √3