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So how does cos(x)=sin(x) can be rearranged to be tan(x)=1

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1 Answer

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Divide by cos(x) on both sides.

If cos(x) is not zero, or equivalently, if x in not an odd integral multiple of pi/2, sin(x)/cos(x) equals tan(x), and hence from your equations, tan(x)=1.

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