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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= cot (2 a)

We showed that the two sides could take the same form

\Rightarrow True

sec (t) = \frac{cot ( t ) + tan ( t )}{csc ( t )}

\frac{1 - cos ( 2 a )}{sin ( 2 a )} = tan (a)

sin (2 x) + sin (x) = sin (3 x)

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

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

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