Is 1/2 cot(x)-1/2 tan(x)=cot(2x) ?

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

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prove 1/2 cot(x)-1/2 tan(x)=cot(2x)

prove

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

True

Solution steps

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

Manipulating left side

\frac{1}{2} cot (x) - \frac{1}{2} tan (x)

Express with sin, cos

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

Rewrite using trig identities

= \frac{cos ( 2 x )}{sin ( 2 x )}

Use the basic trigonometric identity:

\frac{cos ( x )}{sin ( x )} = cot (x)

= cot (2 x)

We showed that the two sides could take the same form

\Rightarrow True

cos^{2} (2 x) - sin^{2} (2 x) = 0

cos (x + \frac{π}{6}) = \frac{3}{2} cos (x) - \frac{1}{2} sin (x)

sin^{2} (x) sin^{2} (x) = sin^{4} (x)

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

cos (- 2 θ) = cos (2 θ)

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