Question

If cos (A+B) = 1/2 and sin ( A-B) = 1/2, then find the values of A and B where A and B are acute angles.​

Answer 1

Step-by-step explanation:

cos(A+B ) = 1/2

sin(A- B ) = 1/2

R.H.S are equal so,L.H.S also equal

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

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

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

90 - A- B = A - B

90 = 2A

A= 45

A + B= 90

45 + B =90

B = 90 - 45

B = 45