Is (cos^2(-x)csc(x))/(cot(x))=cos(x) ?

The answer to whether (cos^2(-x)csc(x))/(cot(x))=cos(x) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove (cos^2(-x)csc(x))/(cot(x))=cos(x)

prove

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

True

Solution steps

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

Manipulating left side

\frac{cos ^{2} ( - x ) csc ( x )}{cot ( x )}

Use the negative angle identity:

cos (- x) = cos (x)

= \frac{cos ^{2} ( x ) csc ( x )}{cot ( x )}

Express with sin, cos

\frac{cos ^{2} ( x ) csc ( x )}{cot ( x )}

Use the basic trigonometric identity:

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

= \frac{cos ^{2} ( x ) \frac{1}{s i n ( x )}}{cot ( x )}

Use the basic trigonometric identity:

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

= \frac{cos ^{2} ( x ) \frac{1}{s i n ( x )}}{\frac{c o s ( x )}{s i n ( x )}}

Simplify

\frac{cos ^{2} ( x ) \frac{1}{s i n ( x )}}{\frac{c o s ( x )}{s i n ( x )}} : cos (x)

\frac{cos ^{2} ( x ) \frac{1}{s i n ( x )}}{\frac{c o s ( x )}{s i n ( x )}}

Apply the fraction rule:

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

= \frac{cos ^{2} ( x ) \frac{1}{s i n ( x )} sin ( x )}{cos ( x )}

Multiply

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

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

Multiply fractions:

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

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

Cancel the common factor:

sin (x)

= 1 \cdot cos^{2} (x)

Multiply:

1 \cdot cos^{2} (x) = cos^{2} (x)

= cos^{2} (x)

= \frac{cos ^{2} ( x )}{cos ( x )}

Cancel the common factor:

cos (x)

= cos (x)

= cos (x)

= cos (x)

We showed that the two sides could take the same form

\Rightarrow True

1 + sin (2 x) = (sin (x) + cos (x))^{2}

sin^{2} (θ) - cos^{2} (θ) sin^{2} (θ) = sin^{4} (θ)

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

(1 + csc (θ)) (1 - csc (θ)) = - cot^{2} (θ)

cot (u) tan (u) - sin^{2} (u) = cos^{2} (u)

Is (cos^2(-x)csc(x))/(cot(x))=cos(x) ?
The answer to whether (cos^2(-x)csc(x))/(cot(x))=cos(x) is True