Question

if sin(A-B)=1/2 and cos (A+B)=1/2 then find the value of A and B​

Answer 1

sin(A−B)=1/2

⇒sin(A−B)=30. [∵sin30 =1/2 ]

On equating both sides

A−B=30 ...(1)

cos(A+B)=1/2

⇒cos(A−B)=cos(60 )[∵cos(60)=1/2]

On equating both sides

A+B=60. ..(2)

Adding (1) and (2)

2A=90

⇒A=45

Putting value of A in (i)

45+B=60

⇒B=15

Hence A=45 ; B=15

Answer 2

Answer:

A=45°, B=15°

Step-by-step explanation:

sin(A-B)=½

sin30°=½

A-B=30°--eq1

cos(A+B)=½

cos60°=½

A+B=60°--eq2

Add eq1 and eq2, we get

2B=30°

B=30°/2

B=15°

Substitute B=15° in eq1

A-B=30°

A-15°=30°

A=30°+15°

A=45°

Therefore, the value of A and B is 45° and 15°.