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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

= sin (x)

We showed that the two sides could take the same form

\Rightarrow True

sin (2 x) = 2 cos (x) sin (x)

cos (x + π) = - cos (x)

sin (x) sec (x) cot (x) = 1

tan (2 u) = \frac{2 cot ( u )}{csc ^{2} ( u ) - 2}

(sin (x))^{2} + (cos (x))^{2} = 1

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