упростите выражение tga/1-tg²a

\\ {tg\alpha\over1-tg^2\alpha}={{sin\alpha\over cos\alpha}\over {cos^2\alpha-sin^2\alpha \over cos^2\alpha}}={sin\alpha \cdot cos\alpha \over cos^2\alpha-sin^2\alpha}={sin\alpha \cdot cos\alpha \over cos^2\alpha-1+cos^2\alpha}={sin\alpha \cdot cos\alpha \over 2cos^2\alpha-1}={tg{2\alpha}\over2}