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Q.
The most general solution of $\tan \theta=-1$ and $\cos \theta=\frac{1}{\sqrt{2}}$ is :
Trigonometric Functions
Solution:
$\tan \theta=-1 \Rightarrow \theta=\frac{3 \pi}{4}, \frac{7 \pi}{4} \text { in }[0,2 \pi] $
$\cos \theta=\frac{1}{\sqrt{2}} \theta=\frac{\pi}{4}, \frac{7 \pi}{4} \text { in }[0,2 \pi] $
common value is $x=\frac{7 \pi}{4}$
general solution is $2 n \pi+\frac{7 \pi}{4}, n \in I$.