Is 2cot(2θ)=cot(θ)-tan(θ) ?

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

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prove 2cot(2θ)=cot(θ)-tan(θ)

prove

2 cot (2 θ) = cot (θ) - tan (θ)

True

Solution steps

2 cot (2 θ) = cot (θ) - tan (θ)

Manipulating left side

2 cot (2 θ)

Express with sin, cos

= \frac{2 cos ( 2 θ )}{sin ( 2 θ )}

Rewrite using trig identities

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

Manipulating right side

cot (θ) - tan (θ)

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

7 cos^{2} (b) - 7 sin^{2} (b) = 14 cos^{2} (b) - 7

0 sec (0) = tan (0)

tan^{3} (x) (csc^{3} (x)) = sec^{3} (x)

sin (x) sec (x) = sin (x)

tan^{2} (y) - sin^{2} (y) = tan^{2} (y) sin^{2} (y)

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