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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

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

Manipulating right side

tan (x) sec (x)

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

sec^{4} (θ) - tan^{4} (θ) = 1 + 2 tan^{2} (θ)

sin (0) tan (0) + cos (0) = sec^{2} (0)

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

sin (3 x) = (sin (x)) (3 - 4 sin^{2} (x))

sec (a) + tan (a) = \frac{1}{sec ( a )} + tan (a)

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