Is cot(2θ)= 1/2 sec(θ)csc(θ)-tan(θ) ?

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

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prove cot(2θ)= 1/2 sec(θ)csc(θ)-tan(θ)

prove

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

True

Solution steps

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

Manipulating right side

\frac{1}{2} sec (θ) csc (θ) - tan (θ)

Express with sin, cos

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

Rewrite using trig identities

= \frac{cos ( 2 θ )}{sin ( 2 θ )}

Use the basic trigonometric identity:

\frac{cos ( x )}{sin ( x )} = cot (x)

= cot (2 θ)

We showed that the two sides could take the same form

\Rightarrow True

csc^{2} (θ) - cos (θ) sec (θ) = cot^{2} (θ)

sin (x) + cos (x) = 1

8 cos^{2} (x) - 8 sin^{2} (x) = 8 - 16 sin^{2} (x)

sec (x) - sin (x) \cdot tan (x) = cos (x)

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

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