Prove that ` cos (45^@-A) cos (45^@- B) -sin(45^@- A)sin (45^@- B) = sin(A+B)`

cos 45^(@)-sin 45^(@)=?

Prove that: i) sin(A+B)cos(A-B)-cos(A+B)sin(A-B)=sin2B ii) cos(45^(@)-A)cos(45^(@)-B)-sin(45^(@)-A)sin(45^(@)-B)=sin(A+B)

Prove that: i) sin(A+B)cos(A-B)-cos(A+B)sin(A-B)=sin2B ii) cos(45^(@)-A)cos(45^(@)-B)-sin(45^(@)-A)sin(45^(@)-B)=sin(A+B)

Prove that: sin 105^@+cos 105^@=cos 45^@

Prove that: sin(45^(@)-A)=1/2cos2A

Show that sin(45^@+A)cos(45^@-B)+cos(45^@+A)cos(45^@-B)=cos(A-B)

Prove that sin105^@+cos105^@=cos45^@

Prove that sin A + cos A= sqrt2 cos (45^@-A)

Prove that sin(45^@+A)sin(45^@-A)=1/2cos2A.

Prove that (cos45^(@)-cos75^(@))/(sin45^(@)+sin75^(@))=2-sqrt3