Prove that `x=sqrt(-1-sqrt(-1-sqrt(-1-…to oo))) =omega or omega^2 `

Prove that sqrt(-1-sqrt(-1-sqrt1-… prop=w or w^2 .

sqrt(-1-sqrt(-1-sqrt(-1......oo))) is equal to

sqrt(-1-sqrt(-1-sqrt(-1oo))) is equal to (where omega is the imaginary cube root of unity and i=sqrt(-1))

the value of sqrt(-1-sqrt(-1-sqrt(-1-...............oo)))

the value of sqrt(-1-sqrt(-1-sqrt(-1-...............oo)))

Prove that: lim_(x rarr oo)x(sqrt(x^(2)+1)-sqrt(x^2-1))) = 1

Prove that: tan^(-1)[(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x+sqrt(1-x)))]=(pi)/(4)-(1)/(2)cos^(-1)x,quad -(1)/(sqrt(2))<=x<=1

If y=sqrt(x+sqrt(x+sqrt(+…..oo))) then prove that (2y-1)dy/dx=1.

Prove that tan^(-1)((sqrt(1+x)-sqrt(1-sin x))/(sqrt(1+x)-sqrt(1-sin x)))=(pi)/(4)-(1)/(2)cos^(-1),-(1)/(sqrt(2))<=x<=1