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Question

The general solution of the equation sin2x+2sinx+2cosx+1=0 is

A
3nππ4
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B
2nπ+π4
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C
2nπ+(1)nsin1(13)
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D
nππ4
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Solution

The correct option is D nππ4
Given, sin2x+2sinx+2cosx+1=0

1+sin2x+2(sinx+cosx)=0

sin2x+cos2x+2sinxcosx+2(sinx+cosx)=0

(sinx+cosx)2+2(sinx+cosx)=0

(sinx+cosx)(sinx+cosx+2)=0

sinx+cosx=0 or sinx+cosx=2

But, sinx+cosx=2 is inadmissible.

Since, |sinx|1,|cosx|1

Therefore, sinx+cosx=0

sin(x+π4)=0

x+π4=nπ

x=nππ4

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