Is cot(2x)= 1/2 (cot(x)-tan(x)) ?

The answer to whether cot(2x)= 1/2 (cot(x)-tan(x)) is True

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prove cot(2x)= 1/2 (cot(x)-tan(x))

prove

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

True

Solution steps

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

Manipulating right side

\frac{1}{2} (cot (x) - tan (x))

Express with sin, cos

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= cot (2 x)

We showed that the two sides could take the same form

\Rightarrow True

(csc^{2} (x) - 1) (sec^{2} (x) - 1) = 1

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

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

\frac{csc ( x ) - cot ( x )}{csc ( x )} = 1 - cos (x)

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

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