Question

If sin(A-B) = 1/2 and cos (A+B) = 1/2, 0°<(A+B)≤90°,A>B.Find A and B.

Answer 1

Answer:

A = 45°

B = 15°

Step-by-step explanation:

sin(A-B) = 1/2 = sin 30°

Therefore, A-B = 30

A= 30 + B .....(i)

cos(A+B)= 1/2 = cos 60°

A+B = 60°

30 + B + B = 60 [Substituting equation (i)]

2B = 60-30 = 30

B=15°

A - B = 30°

A - 15° = 30°

A = 45°

I hope this helps!

Answer 2

Step-by-step explanation:

sin A-B = sin 30

A-B=30                   eq 1

cos A+B = cos 60

A+B = 60                    eq 2

ELIMINATION METHOD

A-B=30

A+B=60

2a=90

A=45

A=45 in eq 1

45-B=30

B=45-30

B=15

ANS A=45 B=15