# minimum value of cos(cosx) is what , with explanation

Jayakrishna Natarajan
39 Points
7 years ago
let y=cos(cosx)
dy/dx= sin(cosx)*sinx... dy/dx=0 @ x=2n(pi) or 2m+1(pi/2)
substituting this value for y..
y=cos1 or y=1
therefore range of y is [cos1,1]
jagdish singh singh
173 Points
7 years ago
$\hspace{-0.6 cm} Let f(x)=\cos (\cos x)\;\forall x\in \mathbb{R}. Using -1 \leq \cos x\leq 1\\\\ So \cos 1 \leq \cos (\cos x)\leq 1., Bcz \cos x is an Decreasing function \\\\So above we have reverse Inequality and it is also an even function.\\\\So its value is same at two end points \bf{i.e \; \cos(-1) = \cos (1)}\\\\and Max. of \cos is \bf{1}. So f(x)=\cos(\cos x)\in \left[\cos 1\;, 1\right].$
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