Answer: -1/2
Step-by-step explanation:
Use double-angle identities:
cos(2θ)=cos^2θ−sin2^θ
cos(2θ)=1−2sin^2θ
cos(2θ)=2cos^2θ−1
sin(x)=1/2
cos(2x)=1−2sin^2x=1−2(1/4)=1/2
cos(4x)=2cos2^(2x)−1=2(1/4)−1=-1/2
Answer: cos4x=-1/2 if sinx=1/2.
[tex]sinx=\frac{1}{2}\\ x=\frac{\pi }{6} .\\4x=4*\frac{\pi }{6}=\frac{2\pi }{3}.\\ cos4x=cos\frac{2\pi }{3}=-\frac{1}{2} .[/tex]
