Question Number 75617 by mathocean1 last updated on 13/Dec/19
![Demonstrate that ∀ x ∈]0;(π/2)[ tanx=((1−cos(2x))/(sin(2x)))](https://www.tinkutara.com/question/Q75617.png)
$$\left.\mathrm{Demonstrate}\:\mathrm{that}\:\forall\:\mathrm{x}\:\in\right]\mathrm{0};\frac{\pi}{\mathrm{2}}\left[\right. \\ $$$$\mathrm{tanx}=\frac{\mathrm{1}−\mathrm{cos}\left(\mathrm{2x}\right)}{\mathrm{sin}\left(\mathrm{2x}\right)} \\ $$
Commented by mind is power last updated on 13/Dec/19
$$\mathrm{use}\:\mathrm{cos}\left(\mathrm{2x}\right)=\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} \left(\mathrm{x}\right) \\ $$$$\mathrm{and}\:\mathrm{sin}\left(\mathrm{2x}\right)=\mathrm{2sin}\left(\mathrm{x}\right)\mathrm{cos}\left(\mathrm{x}\right) \\ $$