Is cot(-x)sin(x)=-cos(x) ?

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

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

prove

cot (- x) sin (x) = - cos (x)

True

Solution steps

cot (- x) sin (x) = - cos (x)

Manipulating left side

cot (- x) sin (x)

Use the negative angle identity:

cot (- x) = - cot (x)

= (- cot (x)) sin (x)

Express with sin, cos

(- cot (x)) sin (x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

Remove parentheses:

(- a) = - a

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

Multiply fractions:

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

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

Cancel the common factor:

sin (x)

= - cos (x)

= - cos (x)

= - cos (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 + tan ^{2} ( x )}{1 - tan ^{2} ( x )} = sec (2 x)

sin (3 π - x) = sin (x)

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

sin (3 x) = 4 sin (x) cos^{2} (x) - sin (x)

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