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Answer :

we have the equation

tan(x) (tan x + 1) = 0

this equation is satisfied when

tan(x)=0

and

(tanx+1)=0

Remember that

the tanx is zero when the sine is zero

so

x=0,pi, 2pi,3pi,...

x=(+/-)npi

and

(tanx+1)=0

when

the value of tanx=-1

so

x=-pi/4 --------> pi/4(+/-)npi

therefore

the answer is option A

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