Derivation for sum of angles

sinCos

Cos(A+B)=OP/OS=(OQ-PQ)/OS
	=OQ/OS-PQ/OS
	=OQ/OR*OR/OS-PQ/SR*SR/OS
	=CosA*CosB-SinA*SinB …………(since PQ=TR)
Sin(A+B)=SP/OS=(ST+TP)/OS
	=ST/OS+TP/OS
	=ST/SR*SR/OS+TP/OR*OR/OS
	=CosA*SinB +SinA*CosB	………..(since TP=RQ)
Tan(A+B)=Sin(A+B)/Cos(A+B)
	=(SinA*CosB+CosA*SinB)/(CosA*CosB-SinA*SinB)
	=(TanA+TanB)/(1-TanA*TanB)………(dividing both side by CosA*CosB) 

For A-B note that sin is odd function and cos is even function, therefore, Sin(-A)=-SinA and Cos(-A)=Cos(A). Graphically this means the cos function is symmetric over x axis while sine function is not so.

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