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

csc (x) - cot (x) = \frac{1}{csc ( x ) + cot ( x )}

cos (π - θ) + sin (\frac{π}{2} + θ) = 0

sin (x) - csc (x) = - cos (x) cot (x)

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

\frac{1}{sin ( x )} = csc (x)

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