Prove that `2cos(pi/16)=sqrt(2+sqrt(2+sqrt(2)))`

1/sqrt2 is

Prove that sqrt i+sqrt(-i)=sqrt 2

Prove that tan (7 1^@/2)=sqrt6-sqrt3+sqrt2-2

Prove that 2sin (5pi/12)cos (pi/12)=(sqrt(3)+2)/2 .

(2+sqrt3)(2-sqrt3) is

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

Prove any one of the following : cos (pi/32)=1/2sqrt[2+sqrt{2+sqrt (2+sqrt 2)}]

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

Prove that cot^(-1) ((sqrt(1+sin x) +sqrt(1-sin x))/(sqrt(1+sin x) -sqrt(1-sinx)))=(x)/(2), x in (0, (pi)/(4)) .

Prove any one of the following: 2 cos 11(1^@)/4=sqrt[2+sqrt(2+sqrt 2)]