Prove the following:`cos(pi/2-x)cos(pi/2-y)-sin(pi/2-x)sin(pi/2-y)=-cos(x+y)`

Prove the following: cos(pi/4-x).cos(pi/4-y)-sin(pi/4-x).sin(pi/4-y)=sin(x+y)

Prove the following: cos(pi/4+x)+cos(pi/4-x)=sqrt2cosx

Prove the following: (frac(cos(pi+x)cos(pi-x))(sin(pi-x)cos(pi/2+x)))=cot^2x

Prove the following: 4cosxcos(pi/3+x)cos(pi/3-x)=cos3x

Prove the following: cos(x+y)cos(x-y)=cos^2y-sin^2x

Prove the following: sin(pi/6+A).cos(pi/3-B)+sin(pi/3-B).cos(pi/6+A)=cos(A-B)

Prove the following: cos(3pi/2+x)cos(2pi+x)[cot(3pi/2-x)+cot(2pi+x)]=1

Select and write the correct answer from the given alternatives in each of the following:If cosycos(pi/2-x)-cos(pi/2-y)cosx+sinycos(pi/2-x)+cosxsin(pi/2-y)=0 then x-y =

Prove the following: (frac(sin^3(pi+x)sec^2(pi-x)tan(2pi-x))(cos^2(pi/2+x)sin(pi-x)cosec^2(-x)))=tan^3x

Solve the following:find the values of sin^2(pi/2)-cos^2(pi/2)+tan^2(pi/2)