Is (cos(x))/(tan(x))=csc(x)-sin(x) ?

The answer to whether (cos(x))/(tan(x))=csc(x)-sin(x) is True

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prove (cos(x))/(tan(x))=csc(x)-sin(x)

prove

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

True

Solution steps

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

Manipulating left side

\frac{cos ( x )}{tan ( x )}

Express with sin, cos

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

Manipulating right side

csc (x) - sin (x)

Express with sin, cos

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

sec^{2} (θ) csc^{2} (θ) = sec^{2} (θ) + csc^{2} (θ)

sin (θ) tan (θ) + cos (θ) = \frac{1}{cos ( θ )}

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

tan (\frac{x}{2}) = \frac{sin ( x )}{1 + cos ( x )}

6 cos^{2} (x) - 6 sin^{2} (x) = 12 cos^{2} (x) - 6

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