<s>[INST] Points of intersection of $\sin x$ and $\cos x$ I'm trying to find the points of intersection of $\sin x$ and $\cos x$ between $0$ and $2\pi$. I've tried but I keep getting 4 solutions... Would someone please be able to take me through the process?
I squared $\sin x$ and $\cos x$ and then got $\sin x = \frac{\pm 1}{\sqrt{2}}$
which gave the solutions $\pi\over 4$, $3\pi \over 4$, $5\pi \over 4$ and $7\pi\over 4$.
 [/INST] $\sin x = \cos x \implies \sin^2x = \cos^2 x $ together with the proviso that $\sin x$ and $\cos x$ must share the same sign.
So the only two solutions are 
$\sin x=\frac{1}{\sqrt 2}$, $\cos x=\frac{1}{\sqrt 2}$ giving $x=\frac{\pi}{4}$
and
$\sin x=\frac{-1}{\sqrt 2}$, $\cos x=\frac{-1}{\sqrt 2}$ giving $x=\frac{5\pi}{4}$
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