# Which of the following functions are strictly decreasing on ?A. cos xB. cos 2xC. cos 3xD. tan x

(A) Let f1(x) = cosx

In interval,

Therefore, f1(x) = cosx is strictly decreasing in interval.

(B) Let f2(x) = cos2x

Now, 0 < x <

0 < 2x < π

sin2x > 0

-2sin2x < 0

Therefore, f2(x) = cos2x is strictly decreasing in interval.

(C) Let f3(x) = cos3x

Now,

sin3x = 0

3x = π, as xϵ

x =

The point x = divides the interval into two distinct intervals.

i.e. and

Now, in interval, ,

f3'(x) = -3sin3x < 0 as (0 < x < => 0 < 3x < π)

Therefore, f3 is strictly decreasing in interval.

Now, in interval

f3'(x)=-3sin3x > 0 as

Therefore, f3 is strictly increasing in interval.

(D) Let f4 = tanx

In interval,

Therefore, f4 is strictly increasing in interval .

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