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Question

If 0x2π and sinx<0, find the correct inequality among the following:
I. cosx<0
II. cosecx<0
III. |sinx+cosx|>0

A
I only
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B
II only
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C
III only
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D
I and II
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E
II and III
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Solution

The correct option is E II and III

0x2π,sinx<0
sinx<0
π<x<2π
Betweenπ<x<2π
cosx0,3π2<x<2π
cosx0,π<x3π2
cscx<1,π<x<2π
sinx+cosx is negative and positive for different values between [π,2π]
Only II is true.

652866_493698_ans_30c81c8f32fc4d6f8347203089612bb8.png

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