Question

If sinx=1/2, find cos4x​

Answer 1

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

Explanation:

`sinx=(1)/(2)\\ x=(\pi )/(6) .\\4x=4*(\pi )/(6)=(2\pi )/(3).\\ cos4x=cos(2\pi )/(3)=-(1)/(2) .`

Answer 2

Answer: -1/2

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