# How you solve for x equation sin(pie times sin x)=cos(pie times cos x)?

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### 1 Answer

`sin(pisinx)=cos(picosx)`

`sin(pisinx)=sin(pi/2-picosx)`

`pisinx=pi/2-picosx`

`sinx=1/2-cosx`

`sinx+sin(pi/2-x)=1/2`

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

`2sin(pi/4)cos(x-pi/4)=1/2`

`sqrt(2)cos(x-pi/4)=1/2`

`cos(x-pi/4)=1/(2sqrt(2))`

`x-pi/4=1.209`

`x=1.209+pi/4=1.995~~2`

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