Question Number 176848 by Ar Brandon last updated on 27/Sep/22
Answered by mr W last updated on 27/Sep/22
$$\beta=\frac{\pi}{\mathrm{2}}−\alpha \\ $$$$\mathrm{cos}\:\left(\frac{\pi}{\mathrm{2}}−\mathrm{2}\beta\right)=\mathrm{sin}\:\mathrm{2}\beta=\mathrm{sin}\:\left(\pi−\mathrm{2}\alpha\right) \\ $$$$=\mathrm{sin}\:\mathrm{2}\alpha=\mathrm{2}\:\mathrm{sin}\:\alpha\:\mathrm{cos}\:\alpha \\ $$$$=\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} } \\ $$