Is (cot(x))/(csc(x)-sin(x))=sec(x) ?

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

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prove (cot(x))/(csc(x)-sin(x))=sec(x)

prove

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

True

Solution steps

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

Manipulating left side

\frac{cot ( x )}{csc ( x ) - sin ( x )}

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{cos ( x )}

Rewrite using trig identities

sec (x)

We showed that the two sides could take the same form

\Rightarrow True

sin (x) = 5 cos (x)

\frac{sin ( 3 x ) + sin ( 5 x )}{cos ( 3 x ) - cos ( 5 x )} = cot (x)

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

2 sin (4 (\frac{5 π}{3})) = 3

sin (a) csc (a) = 1

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