Question

The maximum value of cos(cos(cos(sinx))) for all x belongs to R is​

Answer 1

The maximum value of cos(cos(cos(sinx))) for all x belongs to R is approximately equal to 0.8575, when x = 0

Given,

x belongs to R

To Find,

the maximum value of cos(cos(cos(sinx)))

Solution,

We can solve this using a simple method.

We know that the maximum value that the cos(α) function can assume is 1

This is possible when α=0 or α=2π

Now, maximum value of cos(cos(cos(sinx))) = 1, and this is when cos(cos(sinx)) = 0

Now, cos(cos(sinx)) = 0 when cos(sinx) = π/2

But, we know that cos(x) can't reach π/2 as cos(x) ≤ 1

So, the maximum value of cos(cos(sinx)) is when cos(sin(x)) = 1.

This happens when sin(x) = 0

For this to be true, x = 0

then, cos(cos(cos(sin 0))) = cos(cos(cos 0)) = cos(cos 1) ≈ cos(0.5403) ≈ 0.8575

Therefore the maximum value of cos(cos(cos(sinx))) for all x belongs to R is approximately equal to 0.8575, when x = 0