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Answer» <P> ` sin^(3)x` hasperiod `2pi` and `cos^(4)x` has period `PI`, and L.C.M.of `pi` and `2pi` is `2pi`. Hence, period is `2pi`. (q)` f(x)=sin^(4)x+cos^(4)x,` Both `sin^(4)x` and ` cos^(4)x` have the same period `pi`, and L.C.M. of `pi` and `pi` is `pi`. But `f(x+pi//2)=f(x)`. Then period is `pi//2`. (R) Both `sin^(3)x`and `cos^(3)x` have the same period `2pi,` and L.C.M. of `2pi` and `2pi` is `2 pi`. Hence, period is `2pi, [(f(x+pi) ne f(x)].` (s)`f(x)=cos^(4)x -sin^(4)x` Both `sin^(4)x` and `cos^(4)x` have the same period `pi,` andL.C.M. of `pi` and `pi` is `pi`. Hence, periodis `pi,[f(x+pi//2) ne f(x)].` |
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