The number of all possible ordered pairs `(x, y), x, y in R` satisfying the system of equations `x + y = (2pi)/(3), cos x + cos y = (3)/(2)` is

Options

A. `x = (pi)/(3)-n pi " and " y =n pi, n in Z`
B. `x = n pi " and " y= (pi)/(3)-n pi, n in Z`
C. `x = n pi + (2pi)/(3) "and " y = n pi, n in Z`
D. none of these

Answer

D

Explanation

We have,
`x + y = (2pi)/(3) " "…(i)`
`"and, cos" x+ "cos"y = (3)/(2) " "…(ii)`
Now,
`"cos"x +"cos"y = (3)/(2)`
`rArr 2 "cos" ((x+y)/(2)) "cos" ((x-y)/(2)) = (3)/(2)`
`rArr "cos" ((x-y)/(2)) = (3)/(2))`, which is impossible
Hence, there is no solution.