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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

p ro v e sin (3 π - x) = sin (x)

p ro v e sin^{2} (θ) = \frac{1 - cos ( 2 θ )}{2}

p ro v e (1 + cot (x))^{2} = csc^{2} (x) + 2 cot (x)

p ro v e 1 + tan^{2} (θ) = sec^{2} (θ)

p ro v e \frac{sin ( π - x )}{sin ( x + \frac{π}{2} )} = tan (x)