Is tan(2x)-2cos(x)=0 ?

The answer to whether tan(2x)-2cos(x)=0 is False

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prove tan(2x)-2cos(x)=0

prove

tan (2 x) - 2 cos (x) = 0

False

Solution steps

tan (2 x) - 2 cos (x) = 0

Show that the two sides are not equal

For

tan (2 x) - 2 cos (x) = 0

plug in

x = 0

tan (2 \cdot 0) - 2 cos (0) = - 2

tan (2 \cdot 0) - 2 cos (0)

Simplify

= tan (0) - 2 cos (0)

Use the following trivial identity:

tan (0) = 0

tan (0)

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 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

= 0 - 2 \cdot 1

Simplify

= - 2

The two sides are not equal

\Rightarrow False