Is (1-tan(x))/(sin(x))=csc(x)-sec(x) ?

The answer to whether (1-tan(x))/(sin(x))=csc(x)-sec(x) is True

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prove (1-tan(x))/(sin(x))=csc(x)-sec(x)

prove

\frac{1 - tan ( x )}{sin ( x )} = csc (x) - sec (x)

True

Solution steps

\frac{1 - tan ( x )}{sin ( x )} = csc (x) - sec (x)

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

csc (x) - sec (x)

We showed that the two sides could take the same form

\Rightarrow True

sec (θ) sin (θ) cot (θ) = 1

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

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

csc (θ) cos^{2} (θ) + sin (θ) = csc (θ)

sec (θ + \frac{π}{2}) = csc (θ)

Is (1-tan(x))/(sin(x))=csc(x)-sec(x) ?
The answer to whether (1-tan(x))/(sin(x))=csc(x)-sec(x) is True