Is sec^2(x)=(csc(x))/(csc(x)-sin(x)) ?

The answer to whether sec^2(x)=(csc(x))/(csc(x)-sin(x)) is True

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prove sec^2(x)=(csc(x))/(csc(x)-sin(x))

prove

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

True

Solution steps

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

Manipulating left side

sec^{2} (x)

Express with sin, cos

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

Rewrite using trig identities

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

Manipulating right side

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

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{cos ( θ )}{sin ( θ )} = cot (θ)

\frac{cot ^{2} ( θ )}{csc ( θ )} = csc (θ) - sin (θ)

cos (4 x) = 2 cos^{2} (2 x) - 1

- cos (x) tan (x) = - sin (x)

\frac{sin ( 2 a )}{1 - cos ( 2 a )} = cot (a)

Is sec^2(x)=(csc(x))/(csc(x)-sin(x)) ?
The answer to whether sec^2(x)=(csc(x))/(csc(x)-sin(x)) is True