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

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

Popular >

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

prove

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

True

Solution steps

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

Manipulating left side

- tan (x) cos (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)

Manipulating right side

sin (- x)

Use the negative angle identity:

sin (- x) = - sin (x)

= - sin (x)

We showed that the two sides could take the same form

\Rightarrow True

sin (x - \frac{3 π}{2}) = cos (x)

cos (x + 2 π) = cos (x)

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

\frac{cot ^{2} ( x )}{1 + csc ( x )} = csc (x) - 1

\frac{sin ^{2} ( θ )}{1 - cos ( θ )} = 1 + cos (θ)

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