`tan(x + pi) + 2sin(x + pi) = 0` Find all solutions of the equation in the interval [0, 2pi).

Expert Answers
gsarora17 eNotes educator| Certified Educator

`tan(x+pi)+2sin(x+pi)=0 , 0<=x<=2pi`

using `tan(x+pi)=tan(x) , sin(x+pi)=-sin(x)`





solving each part separately,

`sin(x)=0 , (1-2cos(x))=0`

For sin(x)=0,

General solutions are,

`x=0+2pin , x=pi+2pin`

solutions for the range `0<=x<=2pi`  are,




General solutions for cos(x)=1/2 are,

`x=pi/3+2pin, (5pi)/3+2pin`

Solutions for the range `0<=x<=2pi`  are,

`x=pi/3 , (5pi)/3`

combine all the solutions,