\frac{2 tan ( x )}{1 + tan ^{2} ( x )}

$tan (v) = \frac{sin ( v )}{cos ( v )}$

\frac{2 ( \frac{s i n ( x )}{c o s ( x )} )}{1 + ( \frac{s i n ( x )}{c o s ( x )} ) ^{2}}

$(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}$

\frac{2 ( \frac{s i n ( x )}{c o s ( x )} )}{1 + \frac{s i n ^{2} ( x )}{c o s ^{2} ( x )}}

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Förenkla

Skriv $1$ som $\frac{cos ^{2} ( x )}{cos ^{2} ( x )}$

\frac{2 ( \frac{s i n ( x )}{c o s ( x )} )}{\frac{c o s ^{2} ( x )}{c o s ^{2} ( x )} + \frac{s i n ^{2} ( x )}{c o s ^{2} ( x )}}

Addera bråk

\frac{2 ( \frac{s i n ( x )}{c o s ( x )} )}{\frac{c o s ^{2} ( x ) + s i n ^{2} ( x )}{c o s ^{2} ( x )}}

Kommutativa lagen för addition

\frac{2 ( \frac{s i n ( x )}{c o s ( x )} )}{\frac{s i n ^{2} ( x ) + c o s ^{2} ( x )}{c o s ^{2} ( x )}}

$sin^{2} (v) + cos^{2} (v) = 1$

\frac{2 ( \frac{s i n ( x )}{c o s ( x )} )}{\frac{1}{c o s ^{2} ( x )}}

$\frac{a}{b / c} = \frac{a \cdot c}{b}$

\frac{2 ( \frac{s i n ( x )}{c o s ( x )} ) \cdot cos ^{2} ( x )}{1}

$\frac{a}{1} = a$

2 (\frac{sin ( x )}{cos ( x )}) \cdot cos^{2} (x)

Ta bort parentes

2 \cdot \frac{sin ( x )}{cos ( x )} \cdot cos^{2} (x)

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

2 \cdot \frac{sin ( x ) \cdot cos ^{2} ( x )}{cos ( x )}

Beräkna kvot

2 \cdot sin (x) \cdot cos (x)

Multiplicera faktorer

2 sin (x) cos (x)

$2 sin (v) cos (v) = sin (2 v)$

sin (2 x)

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