Question

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

Answer 1

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)))`