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

sin^{2} (x) + 4 cos^{2} (x) = 1 + 3 cos^{2} (x)

sec (a) - \frac{cos ( a )}{1 + sin ( a )} = tan (a)

\frac{1}{cos ( x ) csc ( x )} = tan (x)

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

1 - cos (2 x) = 2 sin^{2} (x)

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