Is cot(2θ)=((cot^2(θ)-1))/(2cot(θ)) ?

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

= \frac{cos ^{2} ( θ ) - 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

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

\frac{1}{tan ( θ )} = cot (θ)

tan (2 x) cos (2 x) = sin (2 x)

tan (x) = 2 sin (x)

\frac{1 - sin ^{4} ( a )}{cos ^{2} ( a )} = 2 - cos^{2} (a)

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