Solve `(sqrt(5)-1)/(sinx)+(sqrt(10+2sqrt(5)))/(cosx)=8,x in (0,pi/2)`

Explanation

We have `(sqrt(5)-1)/4xx1/(sin x)+sqrt(10+2sqrt(5))/4xx1/(cos x)=2`
`rArr ((sqrt(5)-1))/4 cos x + sqrt(10+2sqrt(5))/4sin x=2 sin x. cos x`
`rArr sin (x+pi/10)=sin 2x or sin (x+pi/10)= sin (pi-2x)`
`rArr x+pi/10=2x" "or x+pi/10=pi-2x`
`rArr x=pi/10" "or 3x=pi-pi/10=(9pi)/10`
`rArr x=pi/10" "or x=(3pi)/10`