Prove that: `cos((3pi)/4+x)-cos((3pi)/4-x\ )=sqrt(2)sinx`

Prove that: cos((3pi)/(4)+A)-cos((3pi)/(4)-A)=-sqrt(2)sinA

Prove that: cos(pi/4+x)+cos(pi/4-x\ )=sqrt(2)cosx

Prove that: cos(pi/4+x)+cos(pi/4-x)=sqrt(2)\ cos x

Prove that cos(pi/4+x)+cos(pi/4-x)=sqrt(2)cosx .

Prove that: cos(pi/4+A)+cos(pi/4-A)=sqrt(2)cosA

prove that : sin((5pi)/18)-cos((4pi)/9)=sqrt(3)sin(pi/9)

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

Prove that: i) sin(5pi)/(18) - cos(4pi)/(9) = sqrt(3)sinpi/9 ii) cos(3pi)/4+A-cos((3pi)/(4)-A)=-sqrt(2)sinA

Prove that: cos(pi/10)-sin(pi/10)=sqrt(2)sin((3pi)/(20))

Prove that: cos((3pi)/2+x)cos(2pi+x){cot((3pi)/2-x)+"cot"(2pi+x)}=1