Is sec(2θ)=(sec^2(θ)csc^2(θ))/(csc^2(θ)-sec^2(θ)) ?

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

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prove sec(2θ)=(sec^2(θ)csc^2(θ))/(csc^2(θ)-sec^2(θ))

prove

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

True

Solution steps

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

Manipulating right side

\frac{sec ^{2} ( θ ) csc ^{2} ( θ )}{csc ^{2} ( θ ) - sec ^{2} ( θ )}

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{cos ( 2 θ )}

Rewrite using trig identities

sec (2 θ)

We showed that the two sides could take the same form

\Rightarrow True

sin^{2} (x) - 3 cos^{2} (x) = 1 - 4 cos^{2} (x)

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

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

cot (2 θ) = \frac{1}{2} (cot (θ) - tan (θ))

- cot (t) + \frac{sin ( t )}{1 - cos ( t )} = csc (t)

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