The most general values of `theta` satisfying `2"cos" theta + sqrt(3) = 0 "and " sqrt(3) "tan" theta-1 = 0` are given by

Options

A. `n pi +- (pi)/(6), n in Z`
B. `2n pi+-(pi)/(6), n in Z`
C. `2n pi, (7pi)/(6), n in Z`
D. none of these

Answer

C

Explanation

We have
`"cos" theta = -(sqrt(3))/(2) " and tan"theta = (1)/(sqrt(3))`
A value of `theta "in" [0, 2 pi]` satisfying these two equations is `(7pi)/(6)`.
Hence, the general value of `theta` is given by `theta = 2npi + (7 pi)/(6), n in Z`