Is cot(2β)=(cot^2(β)-1)/(2cot(β)) ?

The answer to whether cot(2β)=(cot^2(β)-1)/(2cot(β)) is True

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prove cot(2β)=(cot^2(β)-1)/(2cot(β))

prove

cot (2 β) = \frac{cot ^{2} ( β ) - 1}{2 cot ( β )}

True

Solution steps

cot (2 β) = \frac{cot ^{2} ( β ) - 1}{2 cot ( β )}

Manipulating right side

\frac{cot ^{2} ( β ) - 1}{2 cot ( β )}

Express with sin, cos

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

Rewrite using trig identities

= \frac{cos ( 2 β )}{sin ( 2 β )}

Use the basic trigonometric identity:

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

= cot (2 β)

We showed that the two sides could take the same form

\Rightarrow True

csc^{2} (y) tan^{2} (y) - 1 = tan^{2} (y)

cot (θ) tan (θ) = 1

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

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

(csc^{2} (x) - 1) (sec^{2} (x) - 1) = 1

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