How do you solve $(tan x - 1) (2 sin x + 1) = 0$ $(tanx-1)(2sinx+1)=0$ ?

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How do you solve $(tan x - 1) (2 sin x + 1) = 0$ $(tanx-1)(2sinx+1)=0$ ?

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Answer 1 · 2016-05-15T02:13:43

degrees: $x = 45^{\circ}, 225^{\circ}, 210^{\circ}, 330^{\circ}$ $x=45^@,225^@,210^@,330^@$
radians: $x = \frac{π}{4}, \frac{5}{4} π, \frac{7}{6} π, \frac{11}{6} π$ $x=pi/4,5/4pi,7/6pi,11/6pi$

Explanation:

Given,

$(tan x - 1) (2 sin x + 1) = 0$ $(tanx-1)(2sinx+1)=0$

In order for the equation to equal to $0$ $0$ , either one of the factors must equal to $0$ $0$ . Thus, set each factor to $0$ $0$ and solve for $x$ $x$ . Don't forget about the C.A.S.T. rule!

$tan x - 1 = 0 X X X X X X X 2 sin x + 1 = 0$ $tanx-1=0color(white)(XXXXXXX)2sinx+1=0$

$tan x = 1 X X X X X X X X X sin x = - \frac{1}{2}$ $tanx=1color(white)(XXXXXXXXX)sinx=-1/2$

$x=color(green)(ul(color(black)(45^@)))$ or $color(green)(ul(color(black)(225^@)))color(white)(XXXXXX)x=color(green)(ul(color(black)(210^@)))$ or $color(green)(ul(color(black)(330^@)))$

$color(white)(XXx)color(green)(ul(color(black)(pi/4)))$ or $color(green)(ul(color(black)(5/4pi)))color(white)(XXXXXXXXXx)color(green)(ul(color(black)(7/6pi)))$ or $color(green)(ul(color(black)(11/6pi)))$

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How do you solve $(tan x - 1) (2 sin x + 1) = 0$ $(tanx-1)(2sinx+1)=0$ ?

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How do you solve (tanx-1)(2sinx+1)=0(tanx−1)(2sinx+1)=0(tanx-1)(2sinx+1)=0?

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How do you solve $(tan x - 1) (2 sin x + 1) = 0$ $(tanx-1)(2sinx+1)=0$ ?