18-05-2017
Mathematics

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On interval [0,2pi) cos x=sin x

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LammettHash LammettHash

18-05-2017

[tex]\cos x=\sin x[/tex]

When [tex]\cos x\neq0[/tex], you can divide through by it on both sides to get

[tex]\dfrac{\cos x}{\cos x}=\dfrac{\sin x}{\cos x}\iff 1=\tan x[/tex]

and this occurs for [tex]x=\dfrac\pi4,\dfrac{5\pi}4[/tex].

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