`sin(2x)sin(x) = cos(x)` Find the exact solutions of the equation in the interval [0, 2pi).

Expert Answers

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`sin(2x)sin(x)=cos(x) ,0<=x<=2pi`





solving each part separately,

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

General solutions for cos(x)=0 are,

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

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

`x=pi/2 , x=(3pi/2)`



General solutions are,

`x=pi/4+2pin , x=(3pi)/4+2pin`

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

`x=pi/4 , x=(3pi)/4`



General solutions are,

`x=(5pi)/4+2pin, x=(7pi)/4+2pin`

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

`x=(5pi)/4 , x=(7pi)/4`

Combine all the solutions,

`x=pi/2 ,x=(3pi)/2 , x=pi/4 , x=(3pi)/4 , x=(5pi/4) , x=(7pi)/4`


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