2022 · Q47
If cos (x + y) = 0 and sin (x - y) = (1)/(2), where x, y ϵ [0, (π )/(2)] then what is the value of cot (2x - y)?
Elementary MathematicsTrigonometry
- A0
- B1/2
- C1
- D2
Explanation
cos(x+y) = 0 gives x+y = π/2 and sin(x-y) = 1/2 gives x-y = π/6, so x = π/3, y = π/6. Then cot(2x-y) = cot(π/2) = 0. Hence the keyed option is A.