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  4. If ( cos -1 x)2015>( cos -1 x)2016>( cos -1 x)2017 then x lies in the interval

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Q. If $\left(\cos ^{-1} x\right)^{2015}>\left(\cos ^{-1} x\right)^{2016}>\left(\cos ^{-1} x\right)^{2017}$ then $x$ lies in the interval

Inverse Trigonometric Functions

Solution:

$ t =\cos ^{-1} x $
$t ^{2015}> t ^{2016}> t ^{20117}$
$\therefore t \in(0,1)$
$0< \cos ^{-1} x < 1$
$\text { and } \cos 1< x <1$