THK COMPOUND ANGLE 



29 



clockwise direction, thus producing the compound angle ROM - 

 A- R 



P is a point taken on the line of separation of the angles A 

 and B, and PR is the line drawn perpendicular to OP, meeting 

 the arm of the angle (A 4- B) or (A - B) in R. 



PN and RM are perpendiculars drawn to OX from P and R 

 respectively, while PQ is drawn through P parallel to OX, meeting 

 RM, or RM produced in Q. 



M 



F:G. 11. 



TV. /A , TK 



Then sin (A + B) = 



RM RQ+QM RQ+PN 



OR OR 



RQ PN = RQ RP PN OP 

 ~ OR + OR ~ RP ' OR + OP ' OR 



= cos A sin B + sin A cos B 

 OM ON - MN ON - PQ 





Al /* T\ *U 



Also sin (A - B) = p 



cos(A-B)=< 



2^_!-9. = 2^ 5Z_?Q RP 



OR OR" OP 'OR RP'OR 



cos A cos B sin A sin B 

 RM MQ - QR PN - QR 

 OR " OR OR 



PN_QR _PN OP_QR RP 

 OR " OR ~ OP ' OR ~ RP ' OR 

 sin A cos B cos A sin B 

 ON + NM ON 4- PQ 



OR OR 



ON PQ ON OP PQ RP 



OR + OR " OP ' OR + RP ' OR 



cos A cos B 4- sin A sin B 



OR 



OP PQ 

 OR + RP 



