If f(x)=sin6⁡x+cos6⁡x then range of f (x) is

f(x)=cos6⁡x+sin6⁡x=cos2⁡x+sin2⁡x3−3cos2⁡xsin2⁡xcos2⁡x+sin2⁡x=1−3cos2⁡x1−cos2⁡x=3cos4⁡x−3cos2⁡x+1=3cos4⁡x−cos2⁡x+13=3cos2⁡x−122+112Least value of  f(x) is 14, when cos2⁡x−12=0Greatest value of  f(x) is 1, when cos2⁡x=0 or 1