Question

if sin(A-B)=1/2 cos(A+B)=1/2,0<A≤90, A>B find A and B​

Answer 1

Answer:

A = 45 , B = 15

Step-by-step explanation:

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

Answer 2

Answer:

A = 45 , B = 15 (in degrees)

Step-by-step explanation:

sin (A-B) = 1/2

This means that A-B = 30 deg  as sin30 is 1/2 ......(i)

cos (A+B) = 1/2

This means that A+B = 60 deg as cos60 is 1/2 .......(ii)

adding from both (i) and (ii)

2A = 90 deg

A = 45 deg

Substitute A in either (i) or (ii)

we get B = 15 deg

Take note that answers are in degrees and not radians