Is tan(2u)=(2cot(u))/(csc^2(u)-2) ?

The answer to whether tan(2u)=(2cot(u))/(csc^2(u)-2) is True

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prove tan(2u)=(2cot(u))/(csc^2(u)-2)

prove

tan (2 u) = \frac{2 cot ( u )}{csc ^{2} ( u ) - 2}

True

Solution steps

tan (2 u) = \frac{2 cot ( u )}{csc ^{2} ( u ) - 2}

Manipulating right side

\frac{2 cot ( u )}{csc ^{2} ( u ) - 2}

Express with sin, cos

= \frac{2 cos ( u ) sin ( u )}{1 - 2 sin ^{2} ( u )}

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= tan (2 u)

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

sec (x) - \frac{cos ( x )}{1 + sin ( x )} = tan (x)

tan (x) + cot (x) = (sec (x)) (csc (x))

Is tan(2u)=(2cot(u))/(csc^2(u)-2) ?
The answer to whether tan(2u)=(2cot(u))/(csc^2(u)-2) is True