Find the general values of `theta ` which satisfies the equation ` tan theta =-1 and cos theta =(1)/(sqrt(2))`

Explanation

(i) `tantheta=-1`
`rArr theta=(3pi)/4` of `(7pi)/(4)`
`rArr theta` lies in II or IV quadrants.
Hence, `(3pi)/(4)` and `(7pi)/(4)` are the principles of `theta` satisfying the given equation.
(ii) `costheta=1/2`
`rArr theta=pi/3` or `(5pi)/(3)`
i.e., `theta int I` or IV quadrant
`therefore pi/3` and `(5pi)/(3)` are the principal values of `theta` satisfying the given equation.