Question Number 224065 by MirHasibulHossain last updated on 17/Aug/25
$$\mathrm{Find}\:\mathrm{x},\:\sqrt{\mathrm{3}}\mathrm{x}−\mathrm{3x}\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }=\mathrm{1}\:. \\ $$
Commented by Ghisom_ last updated on 17/Aug/25
![you can only pproximate see question 224029 [ (√3)x−3x(√(1−x^2 ))=1 x=cos θ (√3)cos θ −3cos θ sin θ =1 (√3)cos θ −(3/2)sin 2θ =1 ]](https://www.tinkutara.com/question/Q224068.png)
$$\mathrm{you}\:\mathrm{can}\:\mathrm{only}\:\mathrm{pproximate} \\ $$$$\mathrm{see}\:\mathrm{question}\:\mathrm{224029} \\ $$$$\left[\right. \\ $$$$\sqrt{\mathrm{3}}{x}−\mathrm{3}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }=\mathrm{1} \\ $$$${x}=\mathrm{cos}\:\theta \\ $$$$\sqrt{\mathrm{3}}\mathrm{cos}\:\theta\:−\mathrm{3cos}\:\theta\:\mathrm{sin}\:\theta\:=\mathrm{1} \\ $$$$\sqrt{\mathrm{3}}\mathrm{cos}\:\theta\:−\frac{\mathrm{3}}{\mathrm{2}}\mathrm{sin}\:\mathrm{2}\theta\:=\mathrm{1} \\ $$$$\left.\right] \\ $$