`cos((5pi)/4 - x) = -sqrt(2)/2 (cos(x) + sin(x))` Prove the identity.

Prove the identity `cos((5pi)/4+x)=-sqrt2/2(cos(x)+sin(x))`

Use the formula `cos(u)cos(v)+sin(u)sin(v)`    

on the left side of the equation.

`cos((5pi)/4+x)`

`=cos((5pi)/4)cos(x)+sin((5pi)/4)sin(x)`

`=(-sqrt2/2)cos(x)+(-sqrt2/2)sin(x)`

`=-sqrt2/2(cos(x)+sin(x))`

Prove the identity `cos((5pi)/4+x)=-sqrt2/2(cos(x)+sin(x))`

Use the formula `cos(u)cos(v)+sin(u)sin(v)`    

on the left side of the equation.

`cos((5pi)/4+x)`

`=cos((5pi)/4)cos(x)+sin((5pi)/4)sin(x)`

`=(-sqrt2/2)cos(x)+(-sqrt2/2)sin(x)`

`=-sqrt2/2(cos(x)+sin(x))`