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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

sec^{2} (x) cot^{2} (x) = csc^{2} (x)

sin (θ) + cot (θ) cos (θ) = csc (θ)

cot (θ) + tan (θ) = sec^{(2)} (θ) cot (θ)

csc (x) sec (x) = \frac{sec ^{2} ( x )}{tan ( x )}

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