If sin (A – B) = 1/2, cos(A + B) = 1/2; 0° < A + B < 90°; A > B, f

If sin (A – B) = 12 cos(A + B) = 12; 0° B find A and B.

FullFormDefinition · 2025-10-05T19:57:50.000000Z

If sin (A – B) = 12 cos(A + B) = 12; 0° B find A and B.

1.	If sin (A – B) = 1/2, cos(A + B) = 1/2; 0° < A + B < 90°; A > B, find A and B.
Answer» Given : sin(A - B) = 1/2 ⇒ Sin(A-B) = sin (30^o) [sin (30^o) = 1/2] On equating both the sides, we get A - B = 30^o …(1) And cso (A + B) = 1/2 ⇒ cos(A + B) = cos (60^o) [cos (60^o) = 1/2] On equating both the sides, we get A + B = 60^o …(2) On Adding Eq. (1) and (2), we get 2A = 90^o ⇒ A = 45^o Now, Putting the value of A in Eq.(2), we get 45^o + B =60^o ⇒ B = 15^o Hence, A = 45^o and B = 15^o

Answer»

Given : sin(A - B) = 1/2

⇒ Sin(A-B) = sin (30^o) [sin (30^o) = 1/2]

On equating both the sides, we get

A - B = 30^o …(1)

And cso (A + B) = 1/2

⇒ cos(A + B) = cos (60^o) [cos (60^o) = 1/2]

On equating both the sides, we get

A + B = 60^o …(2)

On Adding Eq. (1) and (2), we get

2A = 90^o

⇒ A = 45^o

Now, Putting the value of A in Eq.(2), we get

45^o + B =60^o

⇒ B = 15^o

Hence, A = 45^o and B = 15^o