Is tan(2x)=-(arctan(-4/3))/2 ?

The answer to whether tan(2x)=-(arctan(-4/3))/2 is False

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prove tan(2x)=-(arctan(-4/3))/2

prove

tan (2 x) = - \frac{arctan ( - \frac{4}{3} )}{2}

False

Solution steps

tan (2 x) = - \frac{arctan ( - \frac{4}{3} )}{2}

Show that the two sides are not equal

For

tan (2 x) = - \frac{arctan ( - \frac{4}{3} )}{2}

plug in

x = 0

tan (2 \cdot 0) = 0

tan (2 \cdot 0)

Simplify

= tan (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

= 0

- \frac{arctan ( - \frac{4}{3} )}{2} = 0.46364 \dots (Degrees : 26.5 7^{\circ})

- \frac{arctan ( - \frac{4}{3} )}{2}

Refine to a decimal form

= 0.46364 \dots

The two sides are not equal

\Rightarrow False

cos (0 + \frac{π}{2}) = - sin (0)

sin^{(2)} (\frac{a}{2}) = \frac{1 - cos ( a )}{2}

\frac{1 + sec ( x )}{tan ( x )} = cot (x) + csc (x)

cot^{2} (x) = \frac{1 + cos ( 2 x )}{1 - cos ( 2 x )}

cos (π + x) = cos (x)

Is tan(2x)=-(arctan(-4/3))/2 ?
The answer to whether tan(2x)=-(arctan(-4/3))/2 is False