Question

sin(A-B)= 1 2 , and cos(A+B)= 1 2 , 0<(A+B)≤900 , then find A and B.

Answer 1

Cos(A+B) = 1/2

⇒cos (A+B) = cos(60)  (as 0<A+B<90)

⇒A+B = 60

sin(A-B) = 1/2

⇒sin(A-B) = sin(30) or sin (150)

⇒A-B = 30 or 150

Case:1

A - B = 30

A + B = 60

Solving we get, A = 45 and B = 15

A>B is satisfied.

Case:2

A - B = 150

A + B = 60

Solving, we get A = 105, B = -45

A>B is satisfied.

So the value of A can be 45 or 105