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Question

For which of the following options, the equality |sinx+cosx|=|sinx|+|cosx| holds TRUE?

A
x can be an angle in I quadrant
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B
x can be an angle in III quadrant
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C
x=nπ,nZ
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D
x=(2n+1)π2,nZ
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Solution

The correct option is D x=(2n+1)π2,nZ
Since, |a+b|=|a|+|b|ab0
So, |sinx+cosx|=|sinx|+|cosx|
sinxcosx0

Possible cases are :
(i) sinx and cosx are of same sign.
i.e., xI quadrant or xIII quadrant.

(ii) sinx=0x=nπ,nZ

(iii) cosx=0x=(2n+1)π2,nZ


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