The most general solution of $\tan \theta =-1,\cos \theta =\frac{1}{\sqrt{2}}$ is

Solution:

We have

$\tan \theta =-1$ and $\cos \theta =\frac{1}{\sqrt{2}}$

The value of $\theta$ lying between 0 and $2\pi$ and satisfying these

is $\frac{7\pi }{4}\text{. }$ Therefore, the most general solution is

$\theta =2n\pi +\frac{7\pi }{4},$ where $n\in Z$