Question

The solution set of the system of equations `x+y=(2pi)/3,cosx+cosy=3/2,` where `xa n dy` are real, is ________
A. `n pi+(-1)^(n)"sin"^(-1)(3)/(2)+(pi)/(6)`
B. `2n pi pm "cos"^(-1)(3)/(2)-(pi)/(6)`
C. no solution
D. none of these

Answer 1

Correct Answer - C
`cos x + cos ((2pi)/(3)-x)=(3)/(2)`
`(cos x)/(2)+(sqrt(3))/(2)sin x = (3)/(2)`
`rArr sin ((pi)/(6)+x)=(3)/(2)` (not possible)