Is cot(θ)-tan(θ)=2cot(2θ) ?

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

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prove cot(θ)-tan(θ)=2cot(2θ)

prove

cot (θ) - tan (θ) = 2 cot (2 θ)

True

Solution steps

cot (θ) - tan (θ) = 2 cot (2 θ)

Manipulating left side

cot (θ) - tan (θ)

Express with sin, cos

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

Rewrite using trig identities

= \frac{cos ( 2 θ ) \cdot 2}{sin ( 2 θ )}

Rewrite using trig identities

2 cot (2 θ)

We showed that the two sides could take the same form

\Rightarrow True

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

cot (2 x) = \frac{sec ( x ) + csc ( x )}{2 sin ( x ) - 2 cos ( x )}

cos^{4} (x) = (1 - sin^{2} (x))^{2}

\frac{\frac{1}{c s c ( x )}}{\frac{1}{c o t ( x )}} = cos (x)

cos (- x) = - cos (x)

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