Is cot(2u)=(cot^2(u)-1)/(2cot(u)) ?

The answer to whether cot(2u)=(cot^2(u)-1)/(2cot(u)) is True

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prove cot(2u)=(cot^2(u)-1)/(2cot(u))

prove

cot (2 u) = \frac{cot ^{2} ( u ) - 1}{2 cot ( u )}

True

Solution steps

cot (2 u) = \frac{cot ^{2} ( u ) - 1}{2 cot ( u )}

Manipulating right side

\frac{cot ^{2} ( u ) - 1}{2 cot ( u )}

Express with sin, cos

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= cot (2 u)

We showed that the two sides could take the same form

\Rightarrow True

\frac{sin ( θ ) csc ( θ )}{cot ( θ )} = tan (θ)

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

sin (θ) = sin^{3} (θ) + cos^{2} (θ) sin (θ)

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

sin^{2} (z) + cos^{2} (z) = 1

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