Is 4*cos(2*x)=1-3*cos(x) ?

The answer to whether 4*cos(2*x)=1-3*cos(x) is False

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prove 4cos(2x)=1-3*cos(x)

Solution

prove

4 \cdot cos (2 \cdot x) = 1 - 3 \cdot cos (x)

Solution

False

Solution steps

4 cos (2 x) = 1 - 3 cos (x)

Show that the two sides are not equal

For

4 cos (2 x) = 1 - 3 cos (x)

plug in

x = 0

4 cos (2 \cdot 0) = 4

4 cos (2 \cdot 0)

Simplify

= 4 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

= 4 \cdot 1

Simplify

= 4

1 - 3 cos (0) = - 2

1 - 3 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

= 1 - 3 \cdot 1

Simplify

= - 2

The two sides are not equal

\Rightarrow False

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Frequently Asked Questions (FAQ)

Is 4*cos(2*x)=1-3*cos(x) ?
The answer to whether 4*cos(2*x)=1-3*cos(x) is False

prove 4*cos(2*x)=1-3*cos(x)

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

Is 4*cos(2*x)=1-3*cos(x) ?

prove 4cos(2x)=1-3*cos(x)

Is 4cos(2x)=1-3*cos(x) ?