Question

If sinx=1/2, find cos4x​

Answer 1

Answer: cos4x=-1/2 if sinx=1/2.

Step-by-step explanation:

$sinx=\frac{1}{2}\\ x=\frac{\pi }{6} .\\4x=4*\frac{\pi }{6}=\frac{2\pi }{3}.\\ cos4x=cos\frac{2\pi }{3}=-\frac{1}{2} .$

Answer 2

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