" Simplest farm of "(2)/(sqrt(2+sqrt(2+sqrt(2+2cos4x))))

Smallest form of 2/(sqrt(2+sqrt(2+sqrt(2+2 cos4x)))) is :

(2)/(sqrt(2) + sqrt(2) + sqrt(2+2 cos 4x)) equals

sec x=(2)/(sqrt(2+(sqrt(2+2cos4x))))

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

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

Prove that secx=2/(sqrt(2+sqrt(2+sqrt(2+2cos8x)))

Simplest form of tan^(-1)((sqrt(1+cos x)+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x))), pi lt x lt (3 pi)/(2) is:

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