Question

If $x=si{n}^{14}\theta +co{s}^{20}\theta$, then write the smallest interval in which the value of x lie.

Answer 1

$sin\theta$ lies between [-1,1]

$si{n}^{14}\theta$ (power is even)will lie between [0,1]Similarly,

$cos\theta$ lies between [-1,1]

$co{s}^{20}\theta$ (power is even)will lie between [0,1]

$si{n}^{14}\theta +co{s}^{20}\theta$ will have maximum value 1.

$(\because$ when $sin\theta =0,cos\theta =1$ and vice a versa)

$\therefore xsi{n}^{14}\theta +co{s}^{20}\theta$ lies in the (0,1] interval.