`cos(x+pi/4)-cos(x-pi/4)=1 , 0<=x<=2pi`

We will use the following identity,

`cos(A+B)=cosAcosB-sinAsinB`

`cos(x+pi/4)-cos(x-pi/4)=1`

`rArr (cos(pi/4)cos(x)-sin(pi/4)sin(x))-(cos(pi/4)cos(x)+sin(pi/4)sin(x))=1`

`rArr(cos(x)-sin(x))/sqrt(2)-(cos(x)+sin(x))/sqrt(2)=1`

`rArr(cos(x)-sin(x)-cos(x)-sin(x))/sqrt(2)=1`

`rArr(-2sin(x))/sqrt(2)=1`

`rArrsin(x)=-1/sqrt(2)`

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`

## Unlock

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

`cos(x+pi/4)-cos(x-pi/4)=1 , 0<=x<=2pi`

We will use the following identity,

`cos(A+B)=cosAcosB-sinAsinB`

`cos(x+pi/4)-cos(x-pi/4)=1`

`rArr (cos(pi/4)cos(x)-sin(pi/4)sin(x))-(cos(pi/4)cos(x)+sin(pi/4)sin(x))=1`

`rArr(cos(x)-sin(x))/sqrt(2)-(cos(x)+sin(x))/sqrt(2)=1`

`rArr(cos(x)-sin(x)-cos(x)-sin(x))/sqrt(2)=1`

`rArr(-2sin(x))/sqrt(2)=1`

`rArrsin(x)=-1/sqrt(2)`

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`