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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.**

⇒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

Solving we get, A = 45 and B = 15

A>B is satisfied.

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

A>B is satisfied.

So the value of A can be

The Brainliest Answer!

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