Is (2cot(x))/(1+cot^2(x))=sin(2x) ?

The answer to whether (2cot(x))/(1+cot^2(x))=sin(2x) is True

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prove (2cot(x))/(1+cot^2(x))=sin(2x)

prove

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

True

Solution steps

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

Manipulating left side

\frac{2 cot ( x )}{1 + cot ^{2} ( x )}

Express with sin, cos

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

Rewrite using trig identities

= sin (2 x)

We showed that the two sides could take the same form

\Rightarrow True

tan^{2} (x) - sin^{2} (x) = tan (x) sin (x)

sec (- x) = - sec (x)

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

cos (x) (tan^{(2)} (x) + 1) = sec (x)

(tan (x) + cot (x)) sin (x) cos (x) = 1

Is (2cot(x))/(1+cot^2(x))=sin(2x) ?
The answer to whether (2cot(x))/(1+cot^2(x))=sin(2x) is True