Is 2cos^2(x)+cos(x)=0 ?

The answer to whether 2cos^2(x)+cos(x)=0 is False

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prove 2cos^2(x)+cos(x)=0

prove

2 cos^{2} (x) + cos (x) = 0

False

Solution steps

2 cos^{2} (x) + cos (x) = 0

Show that the two sides are not equal

For

2 cos^{2} (x) + cos (x) = 0

plug in

x = 0

2 cos^{2} (0) + cos (0) = 3

2 cos^{2} (0) + cos (0)

Use the following trivial identity:

cos (0) = 1

cos (0)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

= 2 \cdot 1^{2} + 1

Simplify

= 3

The two sides are not equal

\Rightarrow False