How do I solve $6 {csc}^{2} x = cot x + 8$ $6csc^2x=cotx+8$ if $o < x < 360$ $o<x<360$ ?

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How do I solve $6 {csc}^{2} x = cot x + 8$ $6csc^2x=cotx+8$ if $o < x < 360$ $o<x<360$ ?

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Answer 1 · 2018-05-15T10:44:08

See below

Explanation:

$6 {csc}^{2} x = cot x + 8$ $6csc^2x=cotx+8$

Using ${csc}^{2} x = 1 + {cot}^{2} x$ $csc^2x= 1+cot^2x$ :
$6 (1 + {cot}^{2} x) = cot x + 8$ $6(1+cot^2x)=cotx+8$

$6 {cot}^{2} x - cot x - 2 = 0$ $6cot^2x-cotx-2=0$

$6 {cot}^{2} - 4 cot x + 3 cot x - 2 = 0$ $6cot^2-4cotx+3cotx-2=0$

$3 cot x (2 cot x + 1) - 2 (2 cot x + 1) = 0$ $3cotx(2cotx+1)-2(2cotx+1)=0$

$cot x = \frac{2}{3}$ $cotx=2/3$
Which is essentially:
$tan x = \frac{3}{2}$ $tanx= 3/2$

$x = arctan (\frac{3}{2}) \approx {56.31}^{\circ} + 180^{\circ} = {236.31}^{\circ}$ $x=arctan(3/2)approx 56.31^@+180^@= 236.31^@$
$x = {56.31}^{\circ}, {236.31}^{\circ}$ $x= 56.31^@, 236.31^@$

$cot x = - \frac{1}{2}$ $cotx= -1/2$
Which is essentially:
$tan x = - 2$ $tanx=-2$

$x = {296.57}^{\circ}, {116.57}^{\circ}$ $x= 296.57^@, 116.57^@$

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How do I solve $6 {csc}^{2} x = cot x + 8$ $6csc^2x=cotx+8$ if $o < x < 360$ $o<x<360$ ?

1 Answer

Explanation:

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