Q.

The solution of x, which satisfy the equation tan3x−tan2x1+tan3x.tanx=1 is

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a

x=nπ+π4,n∈z

b

x=2nπ+π4,n∈z

c

x=nπ+π6,n∈z

d

no value of x

answer is D.

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Detailed Solution

tan3x−tan2x1+tan3xtan2x=1⇒tan(3x−2x)=1⇒tanx=tanπ4⇒x=nπ+π4,n∈IIf n is an integer then 2x=2nπ+π2 and  tan2x  becomes infinite which does not satisfy the given equation∴there is no solution
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