Question

(2+(2+2 cos(4x))^1/2)^1/2 is equal to
-2cosx 0r 2sinx where pi<2x<3pi/2 ?

Answer 1

(2+(2+2 cos(4x))^1/2)^1/2

2+2cos4x= 2(1+cos4x)=4 cos^2 (2x)
(2+2 cos(4x))^1/2= 2 Icos2xI = -2 cos 2x since pi<2x<3pi/2

then (2+(2+2 cos(4x))^1/2)^1/2 = (2-2 cos 2x)^ 1/2= 2 I sin xI = 2 sinx since pi/2<x<3pi/4