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cospi/12-sinpi/12=1/(sqrt(2))...

`cospi/12-sinpi/12=1/(sqrt(2))`

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We have to proof,
`cos((pi)/12)-sin((pi)/12)=1/sqrt(2)`
Let,
L.H.S=`cos((pi)/12)-sin((pi)/12)`
L.H.S=`cos(((pi)/2)-((5pi)/12))-sin((pi)/12)`
L.H.S.=`sin((5pi)/12)-sin(((pi)/2))`
As we know the formula,
`sin(A)-sin(B)= 2[(sin(((A) -(B))/2))(cos(((A)+(B))/2))]`
then, ...
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