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)?23°25°18°12°

Solution

## 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°.

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