Is tan(2θ)=(2cot(θ))/(cot^2(θ)-1) ?

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

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prove tan(2θ)=(2cot(θ))/(cot^2(θ)-1)

prove

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

True

Solution steps

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

Manipulating left side

tan (2 θ)

Express with sin, cos

= \frac{sin ( 2 θ )}{cos ( 2 θ )}

Rewrite using trig identities

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

Manipulating right side

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

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

cos (3 x) - cos (x) = 4 cos^{3} (x) - 4 cos (x)

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

\frac{tan ( A )}{sec ( A )} = sin (A)

tan (8 x) - tan (8 x) tan^{2} (4 x) = 2 tan (4 x)

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

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