Is csc(2θ)= 1/2 sec(θ)csc(θ) ?

The answer to whether csc(2θ)= 1/2 sec(θ)csc(θ) is True

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prove csc(2θ)= 1/2 sec(θ)csc(θ)

prove

csc (2 θ) = \frac{1}{2} sec (θ) csc (θ)

True

Solution steps

csc (2 θ) = \frac{1}{2} sec (θ) csc (θ)

Manipulating left side

csc (2 θ)

Express with sin, cos

= \frac{1}{sin ( 2 θ )}

Rewrite using trig identities

= \frac{1}{2 sin ( θ ) cos ( θ )}

Manipulating right side

\frac{1}{2} sec (θ) csc (θ)

Express with sin, cos

= \frac{1}{2 cos ( θ ) sin ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

sin (x) (1 + cot (x)) = sin (x) + cos (x)

arcsin (x) = \frac{1}{sin ( x )}

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

csc^{2} (x) + sec^{2} (x) = csc^{2} (x) sec^{2} (x)

cos (6 0^{\circ}) = cos^{2} (3 0^{\circ}) - sin^{2} (3 0^{\circ})

Is csc(2θ)= 1/2 sec(θ)csc(θ) ?
The answer to whether csc(2θ)= 1/2 sec(θ)csc(θ) is True