Is prove-tan(θ)cos(θ)=sin(-θ) ?

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

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prove-tan(θ)cos(θ)=sin(-θ)

prove

- tan (θ) cos (θ) = sin (- θ)

True

Solution steps

- tan (θ) cos (θ) = sin (- θ)

Manipulating left side

- tan (θ) cos (θ)

Express with sin, cos

- cos (θ) tan (θ)

Use the basic trigonometric identity:

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

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

Simplify

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

- cos (θ) \frac{sin ( θ )}{cos ( θ )}

Multiply fractions:

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

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

Cancel the common factor:

cos (θ)

= - sin (θ)

= - sin (θ)

= - sin (θ)

Manipulating right side

sin (- θ)

Use the negative angle identity:

sin (- x) = - sin (x)

= - sin (θ)

We showed that the two sides could take the same form

\Rightarrow True

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