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

1 Answer
May 15, 2016

degrees: x=45^@,225^@,210^@,330^@
radians: x=pi/4,5/4pi,7/6pi,11/6pi

Explanation:

Given,

(tanx-1)(2sinx+1)=0

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

tanx-1=0color(white)(XXXXXXX)2sinx+1=0

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)))