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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