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Find all values of \(x\) such that \(0\leq x\leq 2\pi\) and \( \sin(x)-\cos(x) = \dfrac{1}{\sqrt{2}}\).

 

 

been stuck on this for a while now, help would be appreciated!

 Nov 10, 2021
 #1
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$\sin x - \cos x = \frac{1}{\sqrt{2}}$

 

$1 - \sin 2x = \frac{1}{2}$

 

$\sin 2x = \frac{1}{2}$

 

$2x = \frac{\pi}{6}$ or $2x = \frac{5 \pi}{6}$

 

$x = \frac{\pi}{12}$ or $x = \frac{5 \pi}{12}$

 Nov 10, 2021
 #2
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Thanks for answering guest but you need to put your latex in a latex box for it to render properly.

 Nov 12, 2021

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