Question

if sin(A-B)=1/2, cos(A-B)=1/2, find A and B​

Answer 1

Correct Question :-

If sin(A - B)=1/2, cos(A + B)=1/2, find A and B.

Answer :-

The value of A is 45° and value of B is

15°.

Solution :-

i) sin(A - B) = 1/2

⇒ sin(A - B) = sin 30°

Since sin 30° = 1/2

Cancelling sin on both sides

⇒ A - B = 30 --(1)

ii) cos(A + B) = 1/2

⇒ cos(A + B) = cos 60°

Since cos 60° = 1/2

Cancelling cos on both sides

⇒ A + B = 60 --(2)

iii) Subtracting (1) from (2)

⇒ A + B - (A - B) = 60 - 30

⇒ A + B - A + B = 30

⇒ 2B = 30

⇒ B = 30/2

⇒ B = 15

Substitute B = 15 in (1)

⇒ A - B = 30

⇒ A - 15 = 30

⇒ A = 30 + 15

⇒ A = 45

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