2018 · Q64
Let sin(A + B) = √3/2 and cos B = √3/2, where A and B are acute angles. What is tan(2A − B) equal to?
Elementary MathematicsTrigonometry
- A1/2
- B√3
- C1/√3
- D1
Explanation
cos B = sqrt(3)/2 with B acute gives B = 30 degrees. sin(A + B) = sqrt(3)/2 with A, B acute gives A + B = 60 degrees (120 degrees is impossible, since A would then be 90 degrees). So A = 30 degrees and tan(2A - B) = tan 30 degrees = 1/sqrt(3). The stored key (D) is wrong. Hence option C.