Is tan(3x)cos(3x)=sin(3x) ?

The answer to whether tan(3x)cos(3x)=sin(3x) is True

prove tan(3x)cos(3x)=sin(3x)

prove

tan (3 x) cos (3 x) = sin (3 x)

True

Solution steps

tan (3 x) cos (3 x) = sin (3 x)

Manipulating left side

tan (3 x) cos (3 x)

Express with sin, cos

cos (3 x) tan (3 x)

Use the basic trigonometric identity:

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

= cos (3 x) \frac{sin ( 3 x )}{cos ( 3 x )}

Simplify

cos (3 x) \frac{sin ( 3 x )}{cos ( 3 x )} : sin (3 x)

cos (3 x) \frac{sin ( 3 x )}{cos ( 3 x )}

Multiply fractions:

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

= \frac{sin ( 3 x ) cos ( 3 x )}{cos ( 3 x )}

Cancel the common factor:

cos (3 x)

= sin (3 x)

= sin (3 x)

= sin (3 x)

We showed that the two sides could take the same form

\Rightarrow True

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Is tan(3x)cos(3x)=sin(3x) ?
The answer to whether tan(3x)cos(3x)=sin(3x) is True