If 1 + $cos x$ $cosx$ - 2 ${sin}^{2} x$ $sin^2x$ = 0 , what is the value of $x$ $x$ ?

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Answer 1 · 2016-06-11T11:33:39

$x = {\pm π + 2 k π} \cup {\pm \frac{π}{3} + 2 k π}$ $x = { pm pi +2k pi} uu {pm pi/3 + 2k pi}$ for $k = 0,pm1,pm2,pm3,...$

Making $sin(x)^2=1-cos(x)^2$ and $y = cos(x)$ we obtain

$1+y-2(1-y^2)=0$

Solving for $y$ we have ${y=-1,y=1/2}$ so the solutions for $x$ must obey

$cos(x) = -1$ or $cos(x) = 1/2$

Solving for $x$ we obtain

$x = pm pi +2k pi$ for $cos(x) = -1$ and
$x = pm pi/3 + 2k pi$ for $cos(x) = 1/2$
for $k = 0,pm1,pm2,pm3,...$

If 1 + cosxcosxcosx - 2sin^2xsin2xsin^2x = 0 , what is the value of xxx?