Question Number 56414 by gunawan last updated on 16/Mar/19
![If for 0<x<(π/2) , y=exp[(sin^2 x+sin^4 x+sin^6 x+...∞)log_e 2] is a zero of the quadratic equation x^2 −9x+8=0, then the value of((sin x+cos x)/(sin x−cos x)) is](https://www.tinkutara.com/question/Q56414.png)
$$\mathrm{If}\:\:\:\mathrm{for}\:\:\mathrm{0}<{x}<\frac{\pi}{\mathrm{2}}\:, \\ $$$$\:{y}={exp}\left[\left(\mathrm{sin}^{\mathrm{2}} {x}+\mathrm{sin}^{\mathrm{4}} {x}+\mathrm{sin}^{\mathrm{6}} {x}+…\infty\right)\mathrm{log}_{{e}} \mathrm{2}\right] \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{zero}\:\mathrm{of}\:\mathrm{the}\:\mathrm{quadratic}\:\mathrm{equation}\: \\ $$$${x}^{\mathrm{2}} −\mathrm{9}{x}+\mathrm{8}=\mathrm{0},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}−\mathrm{cos}\:{x}}\:\mathrm{is} \\ $$