Best solutions to - "I need to prove trigonometric equation tan⁡2x=2sin⁡x⋅cos⁡xcos2x−sin2x"

Shelia Lawrence

Answered question

2021-12-30

I need to prove trigonometric equation

\tan 2 x = \frac{2 \sin x \cdot \cos x}{\cos^{2} x - \sin^{2} x}

esfloravaou

Beginner2021-12-31Added 43 answers

Hints:

\cos 2 x - \sin 2 x = \cos 2 x

2 \sin x \cos x = \sin 2 x

Orlando Paz

Beginner2022-01-01Added 42 answers

Note that

\sin (2 x) = 2 \sin x \cos x

\cos 2 x = \cos^{2} x - \sin^{2} x

nick1337

Expert2022-01-08Added 777 answers

If you know $\sin 2 x = 2 \sin x \cos x$ and $\cos 2 x = \cos^{2} x - \sin^{2} x$
Then $\tan 2 x = \frac{\sin 2 x}{\cos 2 x}$

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