proof of compound angles

COS(A-B)=COSA.COSB+SINA.SINB 1.COS(A-B) Let X`OX AND YOY` be the coordinate axes.Consider a unit circle with O as the centre. Let p1,p2 and p3 be the three points on the circle such that angleXOP1=A,angleXOP2=B and angle XOP3=A-B. As we know that the terminal side of any angle intersects the circle with centre at O and unit radius at a point whose coordinates are the cosine and sine of angle. Chordp0p3=Chordp1p2

SIN(A-B)=SINACOSB-COSASINB SIN(A-B)=COS(90-(A-B)) = COS(90-A)+B) = COS(90-A)COSB-SIN(90-A)SINB = SINACOSB-COSASINB SIN(A+B)=SIN(A-(-B)) =SINA COS(-B)-COSA SIN(-B) =SINA COSB+COSA SINB