33 Prove that the function f(x) = cos x is :

i. strictly decreasing on (0, π)

ii. strictly increasing in (π, 2π)

iii. neither increasing nor decreasing in (0, 2 π)

Given f(x) =cos x

(i) Since for each x (),sin x > 0

⇒

So f is strictly decreasing in (0,)

(ii) Since for each x (),sin x <0

⇒

So f is strictly increasing in (,2)

(iii) Clearly from (1) and (2) above, f is neither increasing nor decreasing in (0,)

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