ddcon4r

2022-07-13

Isolating y in $\mathrm{sin}\left(xy\right)=\mathrm{cos}\left(xy\right)$
Given $\mathrm{sin}\left(xy\right)=\mathrm{cos}\left(xy\right)$, what is the best way to isolate y? Since $\mathrm{sin}\left(\frac{\pi }{2}\right)=\mathrm{cos}\left(\frac{\pi }{2}\right)$ it would seem intuitive to say that $xy=\frac{\pi }{2}$ and thus that $y=\frac{\pi }{2x}$

Kaya Kemp

Expert

Hint:
$\mathrm{tan}\left(xy\right)=1$
and ${\mathrm{tan}}^{-1}$ both sides.

Expert

Thus
$y=\frac{\left(4k+1\right)\pi }{4x}$

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