Question

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TAN^2 X + SQRT3 TAN X =[0}

Answer 1

Explanation:

`tan^2x+√(3) tanx=0\\tanx(tanx+√(3) )=0\\either~tan~x=0=tan~n\pi \\x=n\pi \\where~n~is~an~integer.\\if~x \in[0,2\pi )\\then~x=0,\pi \\or\\tan~x+√(3) =0\\tan~x=-√(3)=tan~(\pi-(\pi )/(3) ),tan~(2\pi -(\pi )/(3) )\\tan~x=tan((2\pi)/(3) ),tan((5\pi)/(3) )\\x=(2\pi )/(3),(5\pi )/(3)`