Question

Solve the equation for solutions over the interval ​[0​°, 360°​).

Answer 1

Answer:

$x=98.13^\circ,135^\circ,278.13^\circ,315^\circ$

Step-by-step explanation:

$tan^2x+7tanx+8=0,[0^{\circ},360^\circ)$

$tan^2x+7tanx+8=0$

$u=tanx$ <-- U-substitution

$u^2+7u+8=0$

$(u+7)(u+1)=0$

$(tanx+7)(tanx+1)=0$ <-- Replace u with tanx

$tanx+7=0$

$tanx=-7$

$x=98.13^\circ,278.13^\circ$

$tanx+1=0$

$tanx=-1$

$x=135^\circ,315^\circ$

Therefore, $x=98.13^\circ,135^\circ,278.13^\circ,315^\circ$