Trigonometry (C10)

If sin (A + 2B) = √3/2 and cos (A + 4B) = 0, A > B, and A + 4B ≤ 90º, then find A and B.

Answer

sin (A + 2B) = √3/2

⇒ A + 2B = 60º

cos (A + 4B) = 0

⇒ A + 4B = 90°

Solving, we get A = 30°, B = 15°