Is (sin(x)cos(x))/(1-cos^2(x))=cot(x) ?

The answer to whether (sin(x)cos(x))/(1-cos^2(x))=cot(x) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

prove (sin(x)cos(x))/(1-cos^2(x))=cot(x)

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Cancel the common factor:

sin (x)

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

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

Use the basic trigonometric identity:

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

= cot (x)

We showed that the two sides could take the same form

\Rightarrow True

Is (sin(x)cos(x))/(1-cos^2(x))=cot(x) ?
The answer to whether (sin(x)cos(x))/(1-cos^2(x))=cot(x) is True