Question

Find acute angles A and B, if `sin (A + 2B) = sqrt(3)/2` and cos(A + 4B) = 0, A > B.

Answer 1

Sin (A + 2B) = sin 60°

cos (A + 4B) = cos 90°

A + 2B = 60° …(i)

A + 4B = 90° …(ii)

Subtracting (ii) from (i)

A + 4B = 90°

`(-A - 2B = -60)/(2B = 30°)`  ∴ B = 15°

A + 4B = 90°

4B = 4(15°) = 4B = 60°

∴ A + 60° = 90° ∴ A = 30°