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

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

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

prove

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

True

Solution steps

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

Manipulating left side

tan (2 x) cos (2 x)

Express with sin, cos

cos (2 x) tan (2 x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply fractions:

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

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

Cancel the common factor:

cos (2 x)

= sin (2 x)

= sin (2 x)

= sin (2 x)

We showed that the two sides could take the same form

\Rightarrow True

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