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

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

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

prove

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

True

Solution steps

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

Manipulating right side

tan (2 x)

Express with sin, cos

tan (2 x)

Use the basic trigonometric identity:

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

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

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

Rewrite using trig identities

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

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

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

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

We showed that the two sides could take the same form

\Rightarrow True

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