`cos((3pi)/4+x)-sin(pi/4-x)=?`

Prove that: cos((pi)/(4)-x)cos((pi)/(4)-y)-sin((pi)/(4)-x)sin((pi)/(4)-y)=sin(x+y)

Find the rang of f(x)=log_sqrt5(3+cos((3pi)/4+x)+cos((pi)/4+x)+cos((pi)/4-x)-cos((3pi)/4-x))

cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y)=sin(x+y)

Prove the following: (i) cos((3pi)/(4)+x)-cos((3pi)/(4)-x)=-sqrt2 sin x (ii) cos"((pi)/(4)+x)+cos((pi)/(4)-x)=sqrt2 cos x .

prove that sin((pi)/(4)+x)+sin((pi)/(4)-x)=sqrt(2)cos x

cos((3pi)/(4)+x)-cos((3pi)/(4)-x) = -sqrt(2)sinx

Prove that cos((pi)/(4)-x)cos((pi)/(4)+x)=(1)/(2)-sin^(2)x

Using application of trignometric formulas prove that (i)cos(pi/4+x)+cos(pi/4-x)=sqrt2cos x(i1)sin(7pi/12)cos(pi/4)-cos(7pi/12)sin(pi/4)

cos(pi/4-A)cos(pi/4-B)-sin(pi/4-A)sin(pi/4-B)=sin(A+B)