Question

How do you solve `3tan^3x-3=0`?

Answer 1

`x=kpi+pi/4,kinZ`

Explanation:

`3tan^3x-3=0rArr3(tan^3x-1)=0rArrtan^3x-1=0`
`rArr(tanx-1)(tan^2x+tanx+1)=0` `rArr(tanx-1)=0to(1)` `ortan^2x+tanx+1=0to(2)`
`color(red)((1)tanx=1rArrtanx=tan(pi/4)rArrx=kpi+pi/4,kinZ)`
`and color(blue)((2)tan^2x+tanx+1=0)`
Comparing with `ax^2+bx+c=0`,we get `a=1,b=1,c=1rArrtriangle=b^2-4ac=(1)^2-4(1)(1),rArrcolor(red)(triangle=-3< 0rArrtanx!inR)`