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

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

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

prove

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

True

Solution steps

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

Manipulating left side

tan (2 A)

Rewrite using trig identities

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

Simplify

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

sec^{2} (x) - sec^{2} (x) cos^{2} (x) = tan^{2} (x)

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

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

sin (x) tan (x) sec (x) = sec^{2} (x) - 1

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