Question

if sin(A-B)=1/2,cos(A+B)=1/2,0≤A+B≤90,A>B,THEN FIND THE VALUE OF A?

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.

Answer 2

sin(A-B) =1/2
sin(A-B) =sin 30       (bcause 1/2=30)
A-B=30---------------------1
cos(A+B) = 1/2
cos (A+B) =cos 60
A+B = 60-------------------2
Adding 1 and 2 we get 2A = 90
A = 90/2
A= 45
substituting A=45 in 1
A-B = 30
45-B=30
-B=30-45
-B=-15
B=15