# Which of the foll

(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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