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

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

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

prove

cot (x) - 1 = csc (x) (cos (x) - sin (x))

True

Solution steps

cot (x) - 1 = csc (x) (cos (x) - sin (x))

Manipulating left side

cot (x) - 1

Express with sin, cos

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

Use the basic trigonometric identity:

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

= (cos (x) - sin (x)) csc (x)

= csc (x) (cos (x) - sin (x))

We showed that the two sides could take the same form

\Rightarrow True

sec (A) csc (A) = 1

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

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

csc (x) = sin (x)

- cos (x) = sin (x + \frac{π}{2})

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