Is 2tan(x)=(2sin(x))/(cos(x)) ?

The answer to whether 2tan(x)=(2sin(x))/(cos(x)) is True

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prove 2tan(x)=(2sin(x))/(cos(x))

prove

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

True

Solution steps

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

Manipulating left side

2 tan (x)

Express with sin, cos

2 tan (x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply fractions:

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

Is 2tan(x)=(2sin(x))/(cos(x)) ?
The answer to whether 2tan(x)=(2sin(x))/(cos(x)) is True