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

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

Popular >

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

prove

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

True

Solution steps

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

Manipulating right side

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

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

sec^{2} (x) cot (x) + cot (x) = tan (x)

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

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

1 - sin (r) = sec (r)

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