Question
Tue March 06, 2012 By:
 

State whether sinA+sinB=Sin[a+b] is true or false if not then give reason

Expert Reply
Tue March 06, 2012
It is false .
Reason:
sinA is one quantity , we cant separate sin and A ,
there is no way that we can separate the two sin from their angles and write sin(A+B)
Also when we write {sinA + sinB} its value can be greater than 1 , such as for A = 90 , B = 60 , But Sin(A+B) can only be less than equal to 1 , such as sin150 = 0.5 .
We can always prove that sin(A+B) = sinAcosB + cosAsinB , which can be shown by taking A = 60 , B = 45
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