Range of a function f(x)=cos(k sin x)is [-1,1] then the least positive integral value of k will be?

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Answer 1 · 2018-05-30T15:20:07

$k >= 4$

The range of $ksinx$ is $[-k,k]$ .

As for $x=0$ ,

$cos(ksin(x))|_(x=0) = 1$

The range includes $y=1$ for any value of $k$ .
On the other hand:

$cos(ksinx) = -1 <=> ksinx = pi+2npi$

For $n=0$ :

$ksinx = pi$

and as

$ksinx <= k$

Then $k$ must be greater that $pi$ , which means $k >=4$ .