If x = sin14x + cos20 x, then write the smallest interval in which the value of x lie.
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]