Is prove-cos(x)tan(x)=-sin(x) ?

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

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

prove

- cos (x) tan (x) = - sin (x)

True

Solution steps

- cos (x) tan (x) = - sin (x)

Manipulating left side

- cos (x) tan (x)

Express with sin, cos

- cos (x) tan (x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply fractions:

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

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

Cancel the common factor:

cos (x)

= - sin (x)

= - sin (x)

= - sin (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{sin ( 2 a )}{1 - cos ( 2 a )} = cot (a)

tan (x) cot (x) = sec (x) csc (x)

\frac{cos ( 3 x ) - cos ( 7 x )}{sin ( 3 x ) + sin ( 7 x )} = tan (2 x)

sin (x) sec (x) = \frac{1}{cos ( x ) csc ( x )}

1 + tan (x) = sec (x)

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