Is tan(x+pi)-tan(pi-x)=2tan(x) ?

The answer to whether tan(x+pi)-tan(pi-x)=2tan(x) is True

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prove tan(x+pi)-tan(pi-x)=2tan(x)

prove

tan (x + π) - tan (π - x) = 2 tan (x)

True

Solution steps

tan (x + π) - tan (π - x) = 2 tan (x)

Manipulating left side

tan (x + π) - tan (π - x)

Rewrite using trig identities

= \frac{sin ( x )}{cos ( x )} - tan (π - x)

Rewrite using trig identities

= \frac{sin ( x )}{cos ( x )} - (- \frac{sin ( x )}{cos ( x )})

Simplify

\frac{sin ( x )}{cos ( x )} - (- \frac{sin ( x )}{cos ( x )}) : \frac{2 sin ( x )}{cos ( x )}

= \frac{2 sin ( x )}{cos ( x )}

Rewrite using trig identities

2 tan (x)

We showed that the two sides could take the same form

\Rightarrow True

cot (2 x) = \frac{1}{2 ( cot ( x ) - tan ( x ) )}

\frac{sin ( 6 x )}{cos ( 6 x )} = 6 sin (x)

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

tan (\frac{2 π}{3}) = \frac{\frac{243}{4}}{- \frac{9}{2}}

sec (y) sec (y) = 1

Is tan(x+pi)-tan(pi-x)=2tan(x) ?
The answer to whether tan(x+pi)-tan(pi-x)=2tan(x) is True