value of `sqrt(2+sqrt(2+sqrt(2+sqrt(2+2cos16theta))` where `0 < theta < pi/16`

sqrt(2+sqrt(2+2cos4 theta))

sqrt(2+sqrt(2+2cos4theta))=

Solve sqrt(2+sqrt(2+sqrt(2+2cos16theta)))

sqrt(2+sqrt(2+sqrt(2+2 cos 8 theta)))=

sqrt(2+sqrt(2+2cos4theta))= …………

Prove using induction or otherwise that 2 cos (theta)/(2^(n))=sqrt(2+sqrt(2+sqrt(2…sqrt(2+2cos theta)))) where R.H.S contains n radical signs and 0 in (0, pi)

Prove that sqrt ( 2 + sqrt (2 + sqrt (2 + 2 cos 8 theta))) = 2 cos theta, where theta in [ (-pi)/(8), (pi)/(8)]

Show that sqrt(2+sqrt(2+sqrt(2+2cos 8theta)))=2cos theta

Show that sqrt(2+sqrt(2+sqrt(2+2cos 8theta)))=2cos theta