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Simplify[expr] bug?


I'm a complete newbie to Mathematica and not a math whiz, but the 
results I got from the following two equations seems like bugs to me.

Test 1:
Running: Simplify[Sin(a) - Sin(b)]
Yeilds: (a - b)Sin

Looks like it's treating the function "Sin" like a coefficient

Test 2:
Running: Simplify[d/s + Cos(2*¹*v/s) - Cos(2*¹*(v - 1)/s)]
Yeilds: (d + 2 Cos ¹) / s

Mathematica completely factors out the variable "v" which is critical 
to the correct solution.

Are these bugs or am I making an inadvertent syntax error.

Thanks,

Ken Tozier


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