Question

If cos(A+B) = ½ and sin(A-B) = ½, then find the values of A and B where A and B are acute angles.​

Answer 1

Answer:

A=45°, B=15°

Step-by-step explanation:

cos(A+B) = ½

cos60°=½

A+B=60°--eq1

sin(A-B) = ½

sin30°=½

A-B=30°--eq2

Add eq1 and eq2, we get

2B=30°

B=30°/2

B=15°

Substitute B=15° in eq2

A-B=30°

A-15°=30°

A=30°+15°

A=45°

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