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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)?


  1. 23°

  2. 25°

  3. 18°

  4. 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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