Solve the trigonometric equation $tan^2x+tanx-1=0$ in general and in the interval $[0,2pi)$ ?

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$tan^2x+tanx-1=0$

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Answer 1 · 2017-03-26T16:44:10

$x=nxx180^@+31.7^@$ or
$x=nxx180^@-58.3^@$ ,
where $n$ is an integer
and in ${0,2pi)$ , $x={31.7^@,121.7^@,211.7^@,301.7^@}$

$tan^2x+tanx-1=0$

$:.tanx=(-1+-sqrt(1^2-4xx1xx(-1)))/2$

$=(-1+-sqrt5)/2=(-1+-2.236)/2$

i.e. $-1.618$ or $0.618$

i.e. $x=-58.3^@$ , $x=31.7^@$

Hence $x=nxx180^@+31.7^@$ or $x=nxx180^@-58.3^@$ , where $n$ is an integer

and in ${0,2pi)$ , $x={31.7^@,121.7^@,211.7^@,301.7^@}$