Question

Resolver las siguientes ecuaciones con identidades trigonometricas

a) cos2x - 1/4 =0
b) 3tanx +2 =tan

Answer 1

$\cos \left(2x\right)-\frac{1}{4}=0\\\\\cos \left(2x\right)=\frac{1}{4}\\\\2x=\arccos \left(\frac{1}{4}\right)+2\pi n,\:2x=2\pi -\arccos \left(\frac{1}{4}\right)+2\pi n\\\\x=\frac{\arccos \left(\frac{1}{4}\right)+2\pi n}{2},\:x=\frac{2\pi -\arccos \left(\frac{1}{4}\right)+2\pi n}{2}\\\\x=\frac{1.31812\dots +2\pi n}{2},\:x=\frac{2\pi -1.31812\dots +2\pi n}{2}$

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$3\tan \left(x\right)+2=\tan \left(x\right)\\\\3u+2=u\\\\\tan \left(x\right)=-1\\\\x=\frac{3\pi }{4}+\pi n$

Listo.

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