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

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

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

prove

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

True

Solution steps

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

Manipulating right side

tan (2 x)

Rewrite using trig identities

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

Simplify

\frac{tan ( x ) + tan ( x )}{1 - tan ( x ) tan ( x )} : \frac{2 tan ( x )}{1 - tan ^{2} ( x )}

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

We showed that the two sides could take the same form

\Rightarrow True

sec (x) \frac{tan ( x )}{sin ( x )} = sec^{2} (x)

\frac{1 + tan ^{2} ( θ )}{csc ^{2} ( θ )} = tan^{2} (θ)

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

sin (3 θ) + sin (θ) = 2 sin (θ) cos (θ)

(1 - cos^{2} (a)) (1 + tan^{2} (a)) = tan^{2} (a)

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