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

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

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

prove

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

True

Solution steps

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

Manipulating right side

\frac{csc ( x )}{csc ( x ) - 2 sin ( x )}

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

sec (2 x)

We showed that the two sides could take the same form

\Rightarrow True

(1 - cos^{2} (θ)) (csc^{2} (θ)) = 1

\frac{1}{arctan ( x )} = arccot (x)

\frac{1}{sin ( θ ) cos ( θ )} - tan (θ) = cot (θ)

(- sin (x)) (3 cos (x)) = - 3 sin (x) cos (x)

cot (θ) \cdot sec (θ) = \frac{1}{cos ( θ )}

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