Question

If Sin (A-B) = 1/2 and Cos (A + B) = 1 / 2 0<(A+B)< 90 AB, Then find A and B​

Answer 1

Answer:

Step-by-step explanation:

So first we take sin(A-B) = 30 (since sin 30 = 1/2

Then we take cos (A+B) = 60 since cos 60 =1/2

Now we have two equations

A-B=30

A+B=60

Using elimination method we get that A = 45 and B= 15. Which is the answer

Answer 2

Answer:

sin(A - B) = 1/2 = cos(A + B)

sin(A - B) = cos(A + B)

cos(theta) = sin(90 - theta)

sin(A - B) = sin( 90 -(A+B))

sin(A - B) = sin(90 - A - B))

So, A - B = 90 - A - B

A + A = 90

2A = 90

A = 45°

sin(A - B) = 1/2

as sin 30° = 1/2,

A - B = 30

45 - B = 30

B = 45 - 30

B = 15°