The most general value for which `tantheta=-1costheta=1/(sqrt(2))i s(n in Z)` n`pi+(7pi)/4` (b) `npi+(-1)^n(7pi)/4` `2npi+(7pi)/4` (d) none of these

Options

A. `n pi+(7 pi)/4`
B. `n pi+(-1)^(n) (7pi)/4`
C. `2npi+(7pi)/4`
D. none of these

Answer

C

Explanation

Since `tan theta lt 0` and `cos theta gt 0, theta` lies in the fourth quadrant. Then `theta=7 pi//4`.
Hence, the general value of `theta` is `2n pi+7 pi//4, n in Z`.