Is tan(2θ)=(2tan(θ))/(1-tan^2(θ)) ?

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

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prove tan(2θ)=(2tan(θ))/(1-tan^2(θ))

prove

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

True

Solution steps

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

Manipulating left side

tan (2 θ)

Rewrite using trig identities

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

Simplify

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

(csc (x) + cot (x)) (csc (x) - cot (x)) = 1

cot^{2} (θ) - csc^{2} (θ) = - 1

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