Question

If sin (2A − 3B) = cos (3A + 8B), where (2A − 3B) and (3A + 8B) are acute angles, then what is the value of (A + B)?

• A. 25°
• B. 23°
• C. 18°
• D. 12°

Answer 1

The correct option is C

18°

It is given that sin (2 − 3) = cos (3 + 8).

Since (2 − 3) is an acute angle, sin (2 − 3) = cos {90° − (2 − 3)}.

∴cos {90° − (2 − 3)} = cos (3 + 8)

Since {90° − (2 − 3)} and (3 + 8) are both acute angles, we have

⇒ 90° − 2 + 3 = 3 + 8

⇒ 5 + 5 = 90°

⇒ 5( + ) = 90°

⇒ ( + ) =

Thus, the value of ( + ) is 18°.