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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= \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

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

3 sin (9 π - x) = 3 sin (x)

sin^{2} (x) = sin (x) sin (x)

(1 - tan^{2} (x)) (1 + tan^{2} (x)) = cos (2 x)

sin (0) sec (0) = tan (0)

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