Is (cot(θ)-tan(θ))/(cot(θ)+tan(θ))=cos(2θ) ?

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

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prove (cot(θ)-tan(θ))/(cot(θ)+tan(θ))=cos(2θ)

prove

\frac{cot ( θ ) - tan ( θ )}{cot ( θ ) + tan ( θ )} = cos (2 θ)

True

Solution steps

\frac{cot ( θ ) - tan ( θ )}{cot ( θ ) + tan ( θ )} = cos (2 θ)

Manipulating left side

\frac{cot ( θ ) - tan ( θ )}{cot ( θ ) + tan ( θ )}

Express with sin, cos

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

Rewrite using trig identities

= cos (2 θ)

We showed that the two sides could take the same form

\Rightarrow True

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

cos (x) (sec (x) - 1) = 1 - cos (x)

3 sec^{2} (33 0^{\circ}) tan (33 0^{\circ}) = 4 tan (33 0^{\circ})

(sin (x)) (cot (x)) = (cos (x))

- 2 sin (x) cos (x) = - sin (2 x)

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