Question

[Nguyễn Minh Đức]

a)sin^4\(\frac{x}{3}\) +cos^4\(\frac{x}{3}\)=\(\frac{5}{8}\)

b)4(sin^4x+cos^4x)+\(\sqrt{3}\)sin4x=2

c)cos^4x+sin^6x=cos2x

d)cos^6x+sin^6x=cos4x

2cos^2x+2cos^2x+4cos^3(2x)-3cos2x=5

Answer 1

[Nguyễn Minh Đức]

2cos^2x+2cos^2(2x)+4cos^3(2x)-3cos2x=5

Answer 2

[Nguyễn Việt Lâm]

e/

\(2cos^2x+2cos^22x+4cos^32x-3cos2x=5\)

\(\Leftrightarrow1+cos2x+2cos^22x+4cos^32x-3cos2x=5\)

\(\Leftrightarrow2cos^32x+cos^22x-cos2x-2=0\)

\(\Leftrightarrow\left(cos2x-1\right)\left(2cos^22x+3cos2x+2\right)=0\)

\(\Leftrightarrow cos2x=1\)

\(\Leftrightarrow x=k\pi\)