# Find the general solution (i) cotθ=−d13 (ii) 4cos2θ=1

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## Answered question

2022-01-30

Find the general solution (i) $\mathrm{cot}\theta =-d\frac{1}{\sqrt{3}}$

(ii) $4{\mathrm{cos}}^{2}\theta =1$

### Answer & Explanation

We know that

$\mathrm{cot}(-\frac{\pi}{3})=-\frac{\sqrt{3}}{3}$

and

$\mathrm{cot}(\theta +\pi )=\mathrm{cot}\theta$

similarly

$\mathrm{cos}\left(\frac{\pi}{3}\right)=\frac{1}{2}$

and

${\mathrm{cos}}^{2}(\theta +\pi )={\mathrm{cos}}^{2}\theta$

therefore

$\left(i\right){\textstyle \phantom{\rule{2em}{0ex}}}x=k\pi -\frac{\pi}{3}$

$\left(ii\right){\textstyle \phantom{\rule{2em}{0ex}}}x=k\pi \pm \frac{\pi}{3}$

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