The most general solution of tan⁡θ=−1,cos⁡θ=12 is

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

1. A

$n\pi +\frac{7\pi }{4},n\in Z$

2. B

$\pi z+\left(-1{\right)}^{n}\frac{7\pi }{4},n\in Z$

3. C

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

4. D

none of these

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### Solution:

We have

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

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

is  Therefore, the most general solution is

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

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