simplify the function y24sin2 x4 into either yAsinBxCD or yA

simplify the function y=2-4sin² (x/4) into either y=Asin(Bx+C)+D or y=Acos(Bx+C)+D

Solution

y = 2 -4sin^2(x/4) into either y=Asin(Bx+C)+D or y=Acos(Bx+C)+D

we know cos2x = 1- 2sin^2x

So, y = 2 - 4(1 -cos(x/2) )/2

= 2 - 2(1 - cos(x/2) )/2

= 1 +cos(x/2)

So, B = 1/2 ; C =0 ; D = 1