Find the period of f(x)=sin^4 x +cos^4 x

Answers (1)

Solution:      We have ,    f(x)=sin^4x+cos^4x

          \ \ Rightarrow hspace1cmf(x)=sin^4x+cos^4x=(sin^2x+cos^2x)^2-2sin^2cos^2x\ \ Rightarrow hspace1cmf(x)=1-frac12sin^22x=1-frac14(1-cos 4x)\ \ Rightarrow hspace1cmf(x)=frac34+frac14sin (4x+fracpi2).

Whence ,              T=frac2piomega=frac2pi4=fracpi2.

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