Answer :

We know the range of sin x is


-1≤ sin x ≤ 1


0≤ sin14x ≤ 1


We know the range of cos x is


-1≤ cos x ≤ 1


0≤ cos20x ≤ 1


0< sin14x + cos20x≤2


which means that the value of x lies in the interval [0,2]


But there's a problem, when sine is 0 cosine is 1, they might even be 0 and -1 at particular points (not in this case, since they are even powers), so the minimum we would get should be more than 0. Hence the value of x lies in (0,1]


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